### (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: Shuffle

### (1) JBC2FIG (SOUND transformation)

Constructed FIGraph.

### (2) Obligation:

FIGraph based on JBC Program:
Graph of 280 nodes with 2 SCCs.

### (3) FIGtoITRSProof (SOUND transformation)

Transformed FIGraph to ITRS rules

### (5) 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:
JMP1821(java.lang.Object(IntList(o973Field0, o973Field1)), java.lang.Object(IntList(o973Field0, o973Field1)), java.lang.Object(IntList(o971, i252)), o990) → Load1484(java.lang.Object(IntList(o973Field0, o973Field1)), java.lang.Object(IntList(o973Field0, o973Field1)), java.lang.Object(IntList(o971, i252)), o990)
Load1484(java.lang.Object(IntList(o973Field0, o973Field1)), java.lang.Object(IntList(o973Field0, o973Field1)), o971, java.lang.Object(IntList(o990, i252))) → Load1484(java.lang.Object(IntList(o973Field0, o973Field1)), java.lang.Object(IntList(o973Field0, o973Field1)), java.lang.Object(IntList(o971, i252)), o990)
Load1484(java.lang.Object(IntList(o993, i253)), java.lang.Object(IntList(o993, i253)), o971, java.lang.Object(IntList(o993, i253))) → JMP1821(java.lang.Object(IntList(o993, i253)), java.lang.Object(IntList(o993, i253)), java.lang.Object(IntList(o971, i253)), o993)
The set Q consists of the following terms:
JMP1821(java.lang.Object(IntList(x0, x1)), java.lang.Object(IntList(x0, x1)), java.lang.Object(IntList(x2, x3)), x4)
Load1484(java.lang.Object(IntList(x0, x1)), java.lang.Object(IntList(x0, x1)), x2, java.lang.Object(IntList(x3, x4)))
Load1484(java.lang.Object(IntList(x0, x1)), java.lang.Object(IntList(x0, x1)), x2, NULL)

### (6) DuplicateArgsRemoverProof (EQUIVALENT transformation)

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

JMP1821(x1, x2, x3, x4) → JMP1821(x2, x3, x4)

### (7) 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:
JMP1821(java.lang.Object(IntList(o973Field0, o973Field1)), java.lang.Object(IntList(o971, i252)), o990) → Load1484(java.lang.Object(IntList(o973Field0, o973Field1)), java.lang.Object(IntList(o971, i252)), o990)
Load1484(java.lang.Object(IntList(o993, i253)), o971, java.lang.Object(IntList(o993, i253))) → JMP1821(java.lang.Object(IntList(o993, i253)), java.lang.Object(IntList(o971, i253)), o993)
The set Q consists of the following terms:
JMP1821(java.lang.Object(IntList(x0, x1)), java.lang.Object(IntList(x2, x3)), x4)

### (8) ITRStoQTRSProof (EQUIVALENT transformation)

Represented integers and predefined function symbols by Terms

### (9) Obligation:

Q restricted rewrite system:
The TRS R consists of the following rules:

JMP1821(java.lang.Object(IntList(o973Field0, o973Field1)), java.lang.Object(IntList(o971, i252)), o990) → Load1484(java.lang.Object(IntList(o973Field0, o973Field1)), java.lang.Object(IntList(o971, i252)), o990)
Load1484(java.lang.Object(IntList(o993, i253)), o971, java.lang.Object(IntList(o993, i253))) → JMP1821(java.lang.Object(IntList(o993, i253)), java.lang.Object(IntList(o971, i253)), o993)

The set Q consists of the following terms:

JMP1821(java.lang.Object(IntList(x0, x1)), java.lang.Object(IntList(x2, x3)), x4)

### (10) DependencyPairsProof (EQUIVALENT transformation)

Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.

### (11) Obligation:

Q DP problem:
The TRS P consists of the following rules:

JMP18211(java.lang.Object(IntList(o973Field0, o973Field1)), java.lang.Object(IntList(o971, i252)), o990) → LOAD1484(java.lang.Object(IntList(o973Field0, o973Field1)), java.lang.Object(IntList(o971, i252)), o990)
LOAD1484(java.lang.Object(IntList(o993, i253)), o971, java.lang.Object(IntList(o993, i253))) → JMP18211(java.lang.Object(IntList(o993, i253)), java.lang.Object(IntList(o971, i253)), o993)

The TRS R consists of the following rules:

JMP1821(java.lang.Object(IntList(o973Field0, o973Field1)), java.lang.Object(IntList(o971, i252)), o990) → Load1484(java.lang.Object(IntList(o973Field0, o973Field1)), java.lang.Object(IntList(o971, i252)), o990)
Load1484(java.lang.Object(IntList(o993, i253)), o971, java.lang.Object(IntList(o993, i253))) → JMP1821(java.lang.Object(IntList(o993, i253)), java.lang.Object(IntList(o971, i253)), o993)

The set Q consists of the following terms:

JMP1821(java.lang.Object(IntList(x0, x1)), java.lang.Object(IntList(x2, x3)), x4)

We have to consider all minimal (P,Q,R)-chains.

### (12) DependencyGraphProof (EQUIVALENT transformation)

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

### (13) Obligation:

Q DP problem:
The TRS P consists of the following rules:

LOAD1484(java.lang.Object(IntList(o993, i253)), o971, java.lang.Object(IntList(o993, i253))) → JMP18211(java.lang.Object(IntList(o993, i253)), java.lang.Object(IntList(o971, i253)), o993)
JMP18211(java.lang.Object(IntList(o973Field0, o973Field1)), java.lang.Object(IntList(o971, i252)), o990) → LOAD1484(java.lang.Object(IntList(o973Field0, o973Field1)), java.lang.Object(IntList(o971, i252)), o990)

The TRS R consists of the following rules:

JMP1821(java.lang.Object(IntList(o973Field0, o973Field1)), java.lang.Object(IntList(o971, i252)), o990) → Load1484(java.lang.Object(IntList(o973Field0, o973Field1)), java.lang.Object(IntList(o971, i252)), o990)
Load1484(java.lang.Object(IntList(o993, i253)), o971, java.lang.Object(IntList(o993, i253))) → JMP1821(java.lang.Object(IntList(o993, i253)), java.lang.Object(IntList(o971, i253)), o993)

The set Q consists of the following terms:

JMP1821(java.lang.Object(IntList(x0, x1)), java.lang.Object(IntList(x2, x3)), x4)

We have to consider all minimal (P,Q,R)-chains.

### (14) 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.

### (15) Obligation:

Q DP problem:
The TRS P consists of the following rules:

LOAD1484(java.lang.Object(IntList(o993, i253)), o971, java.lang.Object(IntList(o993, i253))) → JMP18211(java.lang.Object(IntList(o993, i253)), java.lang.Object(IntList(o971, i253)), o993)
JMP18211(java.lang.Object(IntList(o973Field0, o973Field1)), java.lang.Object(IntList(o971, i252)), o990) → LOAD1484(java.lang.Object(IntList(o973Field0, o973Field1)), java.lang.Object(IntList(o971, i252)), o990)

R is empty.
The set Q consists of the following terms:

JMP1821(java.lang.Object(IntList(x0, x1)), java.lang.Object(IntList(x2, x3)), x4)

We have to consider all minimal (P,Q,R)-chains.

### (16) QReductionProof (EQUIVALENT transformation)

We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].

JMP1821(java.lang.Object(IntList(x0, x1)), java.lang.Object(IntList(x2, x3)), x4)

### (17) Obligation:

Q DP problem:
The TRS P consists of the following rules:

LOAD1484(java.lang.Object(IntList(o993, i253)), o971, java.lang.Object(IntList(o993, i253))) → JMP18211(java.lang.Object(IntList(o993, i253)), java.lang.Object(IntList(o971, i253)), o993)
JMP18211(java.lang.Object(IntList(o973Field0, o973Field1)), java.lang.Object(IntList(o971, i252)), o990) → LOAD1484(java.lang.Object(IntList(o973Field0, o973Field1)), java.lang.Object(IntList(o971, i252)), o990)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.

### (18) Instantiation (EQUIVALENT transformation)

By instantiating [LPAR04] the rule JMP18211(java.lang.Object(IntList(o973Field0, o973Field1)), java.lang.Object(IntList(o971, i252)), o990) → LOAD1484(java.lang.Object(IntList(o973Field0, o973Field1)), java.lang.Object(IntList(o971, i252)), o990) we obtained the following new rules [LPAR04]:

JMP18211(java.lang.Object(IntList(z0, z1)), java.lang.Object(IntList(z2, z1)), z0) → LOAD1484(java.lang.Object(IntList(z0, z1)), java.lang.Object(IntList(z2, z1)), z0)

### (19) Obligation:

Q DP problem:
The TRS P consists of the following rules:

LOAD1484(java.lang.Object(IntList(o993, i253)), o971, java.lang.Object(IntList(o993, i253))) → JMP18211(java.lang.Object(IntList(o993, i253)), java.lang.Object(IntList(o971, i253)), o993)
JMP18211(java.lang.Object(IntList(z0, z1)), java.lang.Object(IntList(z2, z1)), z0) → LOAD1484(java.lang.Object(IntList(z0, z1)), java.lang.Object(IntList(z2, z1)), z0)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.

### (20) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

The remaining pairs can at least be oriented weakly.
Used ordering: Polynomial interpretation [POLO]:

POL(IntList(x1, x2)) = 1 + x1
POL(JMP18211(x1, x2, x3)) = 1 + x2 + x3
POL(LOAD1484(x1, x2, x3)) = 1 + x2 + x3
POL(NULL) = 0
POL(java.lang.Object(x1)) = 1 + x1

The following usable rules [FROCOS05] were oriented: none

### (21) Obligation:

Q DP problem:
The TRS P consists of the following rules:

LOAD1484(java.lang.Object(IntList(o993, i253)), o971, java.lang.Object(IntList(o993, i253))) → JMP18211(java.lang.Object(IntList(o993, i253)), java.lang.Object(IntList(o971, i253)), o993)
JMP18211(java.lang.Object(IntList(z0, z1)), java.lang.Object(IntList(z2, z1)), z0) → LOAD1484(java.lang.Object(IntList(z0, z1)), java.lang.Object(IntList(z2, z1)), z0)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.

### (22) QDPSizeChangeProof (EQUIVALENT transformation)

By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs:

• LOAD1484(java.lang.Object(IntList(o973Field0, o973Field1)), o971, java.lang.Object(IntList(o990, i252))) → LOAD1484(java.lang.Object(IntList(o973Field0, o973Field1)), java.lang.Object(IntList(o971, i252)), o990)
The graph contains the following edges 1 >= 1, 3 > 3

• LOAD1484(java.lang.Object(IntList(o993, i253)), o971, java.lang.Object(IntList(o993, i253))) → JMP18211(java.lang.Object(IntList(o993, i253)), java.lang.Object(IntList(o971, i253)), o993)
The graph contains the following edges 1 >= 1, 3 >= 1, 1 > 3, 3 > 3

• JMP18211(java.lang.Object(IntList(z0, z1)), java.lang.Object(IntList(z2, z1)), z0) → LOAD1484(java.lang.Object(IntList(z0, z1)), java.lang.Object(IntList(z2, z1)), z0)
The graph contains the following edges 1 >= 1, 2 >= 2, 1 > 3, 3 >= 3

### (24) 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:
Load716(java.lang.Object(ARRAY(i3, a481data)), i58, i61) → Load716ARR1(java.lang.Object(ARRAY(i3, a481data)), i58, i61, java.lang.Object(java.lang.String(i91, i90, i92, a610)))
Load716ARR1(java.lang.Object(ARRAY(i3, a481data)), i58, i61, java.lang.Object(java.lang.String(i91, i90, i92, a610))) → Cond_Load716ARR1(i58 > 0 && i58 < i3 && i61 > 0 && i58 + 1 > 0, java.lang.Object(ARRAY(i3, a481data)), i58, i61, java.lang.Object(java.lang.String(i91, i90, i92, a610)))
Cond_Load716ARR1(TRUE, java.lang.Object(ARRAY(i3, a481data)), i58, i61, java.lang.Object(java.lang.String(i91, i90, i92, a610))) → Load716(java.lang.Object(ARRAY(i3, a481data)), i58 + 1, i61 + -1)
The set Q consists of the following terms:
Load716ARR1(java.lang.Object(ARRAY(x0, x1)), x2, x3, java.lang.Object(java.lang.String(x4, x5, x6, x7)))
Cond_Load716ARR1(TRUE, java.lang.Object(ARRAY(x0, x1)), x2, x3, java.lang.Object(java.lang.String(x4, x5, x6, x7)))

### (26) 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:
Load716(java.lang.Object(ARRAY(i3, a481data)), i58, i61) → Load716ARR1(java.lang.Object(ARRAY(i3, a481data)), i58, i61, java.lang.Object(java.lang.String(i91, i90, i92, a610)))
Load716ARR1(java.lang.Object(ARRAY(i3, a481data)), i58, i61, java.lang.Object(java.lang.String(i91, i90, i92, a610))) → Cond_Load716ARR1(i58 > 0 && i58 < i3 && i61 > 0 && i58 + 1 > 0, java.lang.Object(ARRAY(i3, a481data)), i58, i61, java.lang.Object(java.lang.String(i91, i90, i92, a610)))
Cond_Load716ARR1(TRUE, java.lang.Object(ARRAY(i3, a481data)), i58, i61, java.lang.Object(java.lang.String(i91, i90, i92, a610))) → Load716(java.lang.Object(ARRAY(i3, a481data)), i58 + 1, i61 + -1)

The integer pair graph contains the following rules and edges:
(0): LOAD716(java.lang.Object(ARRAY(i3[0], a481data[0])), i58[0], i61[0]) → LOAD716ARR1(java.lang.Object(ARRAY(i3[0], a481data[0])), i58[0], i61[0], java.lang.Object(java.lang.String(i91[0], i90[0], i92[0], a610[0])))
(1): LOAD716ARR1(java.lang.Object(ARRAY(i3[1], a481data[1])), i58[1], i61[1], java.lang.Object(java.lang.String(i91[1], i90[1], i92[1], a610[1]))) → COND_LOAD716ARR1(i58[1] > 0 && i58[1] < i3[1] && i61[1] > 0 && i58[1] + 1 > 0, java.lang.Object(ARRAY(i3[1], a481data[1])), i58[1], i61[1], java.lang.Object(java.lang.String(i91[1], i90[1], i92[1], a610[1])))
(2): COND_LOAD716ARR1(TRUE, java.lang.Object(ARRAY(i3[2], a481data[2])), i58[2], i61[2], java.lang.Object(java.lang.String(i91[2], i90[2], i92[2], a610[2]))) → LOAD716(java.lang.Object(ARRAY(i3[2], a481data[2])), i58[2] + 1, i61[2] + -1)

(0) -> (1), if ((java.lang.Object(java.lang.String(i91[0], i90[0], i92[0], a610[0])) →* java.lang.Object(java.lang.String(i91[1], i90[1], i92[1], a610[1])))∧(i58[0]* i58[1])∧(i61[0]* i61[1])∧(java.lang.Object(ARRAY(i3[0], a481data[0])) →* java.lang.Object(ARRAY(i3[1], a481data[1]))))

(1) -> (2), if ((java.lang.Object(java.lang.String(i91[1], i90[1], i92[1], a610[1])) →* java.lang.Object(java.lang.String(i91[2], i90[2], i92[2], a610[2])))∧(i61[1]* i61[2])∧(i58[1]* i58[2])∧(java.lang.Object(ARRAY(i3[1], a481data[1])) →* java.lang.Object(ARRAY(i3[2], a481data[2])))∧(i58[1] > 0 && i58[1] < i3[1] && i61[1] > 0 && i58[1] + 1 > 0* TRUE))

(2) -> (0), if ((java.lang.Object(ARRAY(i3[2], a481data[2])) →* java.lang.Object(ARRAY(i3[0], a481data[0])))∧(i61[2] + -1* i61[0])∧(i58[2] + 1* i58[0]))

The set Q consists of the following terms:
Load716ARR1(java.lang.Object(ARRAY(x0, x1)), x2, x3, java.lang.Object(java.lang.String(x4, x5, x6, x7)))
Cond_Load716ARR1(TRUE, java.lang.Object(ARRAY(x0, x1)), x2, x3, java.lang.Object(java.lang.String(x4, x5, x6, x7)))

### (27) 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.

### (28) 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): LOAD716(java.lang.Object(ARRAY(i3[0], a481data[0])), i58[0], i61[0]) → LOAD716ARR1(java.lang.Object(ARRAY(i3[0], a481data[0])), i58[0], i61[0], java.lang.Object(java.lang.String(i91[0], i90[0], i92[0], a610[0])))
(1): LOAD716ARR1(java.lang.Object(ARRAY(i3[1], a481data[1])), i58[1], i61[1], java.lang.Object(java.lang.String(i91[1], i90[1], i92[1], a610[1]))) → COND_LOAD716ARR1(i58[1] > 0 && i58[1] < i3[1] && i61[1] > 0 && i58[1] + 1 > 0, java.lang.Object(ARRAY(i3[1], a481data[1])), i58[1], i61[1], java.lang.Object(java.lang.String(i91[1], i90[1], i92[1], a610[1])))
(2): COND_LOAD716ARR1(TRUE, java.lang.Object(ARRAY(i3[2], a481data[2])), i58[2], i61[2], java.lang.Object(java.lang.String(i91[2], i90[2], i92[2], a610[2]))) → LOAD716(java.lang.Object(ARRAY(i3[2], a481data[2])), i58[2] + 1, i61[2] + -1)

(0) -> (1), if ((java.lang.Object(java.lang.String(i91[0], i90[0], i92[0], a610[0])) →* java.lang.Object(java.lang.String(i91[1], i90[1], i92[1], a610[1])))∧(i58[0]* i58[1])∧(i61[0]* i61[1])∧(java.lang.Object(ARRAY(i3[0], a481data[0])) →* java.lang.Object(ARRAY(i3[1], a481data[1]))))

(1) -> (2), if ((java.lang.Object(java.lang.String(i91[1], i90[1], i92[1], a610[1])) →* java.lang.Object(java.lang.String(i91[2], i90[2], i92[2], a610[2])))∧(i61[1]* i61[2])∧(i58[1]* i58[2])∧(java.lang.Object(ARRAY(i3[1], a481data[1])) →* java.lang.Object(ARRAY(i3[2], a481data[2])))∧(i58[1] > 0 && i58[1] < i3[1] && i61[1] > 0 && i58[1] + 1 > 0* TRUE))

(2) -> (0), if ((java.lang.Object(ARRAY(i3[2], a481data[2])) →* java.lang.Object(ARRAY(i3[0], a481data[0])))∧(i61[2] + -1* i61[0])∧(i58[2] + 1* i58[0]))

The set Q consists of the following terms:
Load716ARR1(java.lang.Object(ARRAY(x0, x1)), x2, x3, java.lang.Object(java.lang.String(x4, x5, x6, x7)))
Cond_Load716ARR1(TRUE, java.lang.Object(ARRAY(x0, x1)), x2, x3, java.lang.Object(java.lang.String(x4, x5, x6, x7)))

### (29) ItpfGraphProof (EQUIVALENT transformation)

Applied rule ItpfICap [ICap]

### (30) Obligation:

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

The following domains are used:

Boolean, Integer

R is empty.

The integer pair graph contains the following rules and edges:
(0): LOAD716(java.lang.Object(ARRAY(i3[0], a481data[0])), i58[0], i61[0]) → LOAD716ARR1(java.lang.Object(ARRAY(i3[0], a481data[0])), i58[0], i61[0], java.lang.Object(java.lang.String(i91[0], i90[0], i92[0], a610[0])))
(1): LOAD716ARR1(java.lang.Object(ARRAY(i3[1], a481data[1])), i58[1], i61[1], java.lang.Object(java.lang.String(i91[1], i90[1], i92[1], a610[1]))) → COND_LOAD716ARR1(i58[1] > 0 && i58[1] < i3[1] && i61[1] > 0 && i58[1] + 1 > 0, java.lang.Object(ARRAY(i3[1], a481data[1])), i58[1], i61[1], java.lang.Object(java.lang.String(i91[1], i90[1], i92[1], a610[1])))
(2): COND_LOAD716ARR1(TRUE, java.lang.Object(ARRAY(i3[2], a481data[2])), i58[2], i61[2], java.lang.Object(java.lang.String(i91[2], i90[2], i92[2], a610[2]))) → LOAD716(java.lang.Object(ARRAY(i3[2], a481data[2])), i58[2] + 1, i61[2] + -1)

(0) -> (1), if (((i91[0]* i91[1])∧(i90[0]* i90[1])∧(i92[0]* i92[1])∧(a610[0]* a610[1]))∧(i58[0]* i58[1])∧(i61[0]* i61[1])∧((i3[0]* i3[1])∧(a481data[0]* a481data[1])))

(1) -> (2), if (((i91[1]* i91[2])∧(i90[1]* i90[2])∧(i92[1]* i92[2])∧(a610[1]* a610[2]))∧(i61[1]* i61[2])∧(i58[1]* i58[2])∧((i3[1]* i3[2])∧(a481data[1]* a481data[2]))∧(i58[1] > 0 && i58[1] < i3[1] && i61[1] > 0 && i58[1] + 1 > 0* TRUE))

(2) -> (0), if (((i3[2]* i3[0])∧(a481data[2]* a481data[0]))∧(i61[2] + -1* i61[0])∧(i58[2] + 1* i58[0]))

The set Q consists of the following terms:
Load716ARR1(java.lang.Object(ARRAY(x0, x1)), x2, x3, java.lang.Object(java.lang.String(x4, x5, x6, x7)))
Cond_Load716ARR1(TRUE, java.lang.Object(ARRAY(x0, x1)), x2, x3, java.lang.Object(java.lang.String(x4, x5, x6, x7)))

### (31) IDPNonInfProof (SOUND transformation)

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

For Pair LOAD716(java.lang.Object(ARRAY(i3, a481data)), i58, i61) → LOAD716ARR1(java.lang.Object(ARRAY(i3, a481data)), i58, i61, java.lang.Object(java.lang.String(i91, i90, i92, a610))) the following chains were created:
• We consider the chain LOAD716(java.lang.Object(ARRAY(i3[0], a481data[0])), i58[0], i61[0]) → LOAD716ARR1(java.lang.Object(ARRAY(i3[0], a481data[0])), i58[0], i61[0], java.lang.Object(java.lang.String(i91[0], i90[0], i92[0], a610[0]))) which results in the following constraint:

(1)    (LOAD716(java.lang.Object(ARRAY(i3[0], a481data[0])), i58[0], i61[0])≥NonInfC∧LOAD716(java.lang.Object(ARRAY(i3[0], a481data[0])), i58[0], i61[0])≥LOAD716ARR1(java.lang.Object(ARRAY(i3[0], a481data[0])), i58[0], i61[0], java.lang.Object(java.lang.String(i91[0], i90[0], i92[0], a610[0])))∧(UIncreasing(LOAD716ARR1(java.lang.Object(ARRAY(i3[0], a481data[0])), i58[0], i61[0], java.lang.Object(java.lang.String(i91[0], i90[0], i92[0], a610[0])))), ≥))

We simplified constraint (1) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(2)    ((UIncreasing(LOAD716ARR1(java.lang.Object(ARRAY(i3[0], a481data[0])), i58[0], i61[0], java.lang.Object(java.lang.String(i91[0], i90[0], i92[0], a610[0])))), ≥)∧[(-1)bso_17] ≥ 0)

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

(3)    ((UIncreasing(LOAD716ARR1(java.lang.Object(ARRAY(i3[0], a481data[0])), i58[0], i61[0], java.lang.Object(java.lang.String(i91[0], i90[0], i92[0], a610[0])))), ≥)∧[(-1)bso_17] ≥ 0)

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

(4)    ((UIncreasing(LOAD716ARR1(java.lang.Object(ARRAY(i3[0], a481data[0])), i58[0], i61[0], java.lang.Object(java.lang.String(i91[0], i90[0], i92[0], a610[0])))), ≥)∧[(-1)bso_17] ≥ 0)

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

(5)    ((UIncreasing(LOAD716ARR1(java.lang.Object(ARRAY(i3[0], a481data[0])), i58[0], i61[0], java.lang.Object(java.lang.String(i91[0], i90[0], i92[0], a610[0])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_17] ≥ 0)

For Pair LOAD716ARR1(java.lang.Object(ARRAY(i3, a481data)), i58, i61, java.lang.Object(java.lang.String(i91, i90, i92, a610))) → COND_LOAD716ARR1(&&(&&(&&(>(i58, 0), <(i58, i3)), >(i61, 0)), >(+(i58, 1), 0)), java.lang.Object(ARRAY(i3, a481data)), i58, i61, java.lang.Object(java.lang.String(i91, i90, i92, a610))) the following chains were created:
• We consider the chain LOAD716ARR1(java.lang.Object(ARRAY(i3[1], a481data[1])), i58[1], i61[1], java.lang.Object(java.lang.String(i91[1], i90[1], i92[1], a610[1]))) → COND_LOAD716ARR1(&&(&&(&&(>(i58[1], 0), <(i58[1], i3[1])), >(i61[1], 0)), >(+(i58[1], 1), 0)), java.lang.Object(ARRAY(i3[1], a481data[1])), i58[1], i61[1], java.lang.Object(java.lang.String(i91[1], i90[1], i92[1], a610[1]))), COND_LOAD716ARR1(TRUE, java.lang.Object(ARRAY(i3[2], a481data[2])), i58[2], i61[2], java.lang.Object(java.lang.String(i91[2], i90[2], i92[2], a610[2]))) → LOAD716(java.lang.Object(ARRAY(i3[2], a481data[2])), +(i58[2], 1), +(i61[2], -1)) which results in the following constraint:

(6)    (i91[1]=i91[2]i90[1]=i90[2]i92[1]=i92[2]a610[1]=a610[2]i61[1]=i61[2]i58[1]=i58[2]i3[1]=i3[2]a481data[1]=a481data[2]&&(&&(&&(>(i58[1], 0), <(i58[1], i3[1])), >(i61[1], 0)), >(+(i58[1], 1), 0))=TRUELOAD716ARR1(java.lang.Object(ARRAY(i3[1], a481data[1])), i58[1], i61[1], java.lang.Object(java.lang.String(i91[1], i90[1], i92[1], a610[1])))≥NonInfC∧LOAD716ARR1(java.lang.Object(ARRAY(i3[1], a481data[1])), i58[1], i61[1], java.lang.Object(java.lang.String(i91[1], i90[1], i92[1], a610[1])))≥COND_LOAD716ARR1(&&(&&(&&(>(i58[1], 0), <(i58[1], i3[1])), >(i61[1], 0)), >(+(i58[1], 1), 0)), java.lang.Object(ARRAY(i3[1], a481data[1])), i58[1], i61[1], java.lang.Object(java.lang.String(i91[1], i90[1], i92[1], a610[1])))∧(UIncreasing(COND_LOAD716ARR1(&&(&&(&&(>(i58[1], 0), <(i58[1], i3[1])), >(i61[1], 0)), >(+(i58[1], 1), 0)), java.lang.Object(ARRAY(i3[1], a481data[1])), i58[1], i61[1], java.lang.Object(java.lang.String(i91[1], i90[1], i92[1], a610[1])))), ≥))

We simplified constraint (6) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

(7)    (>(+(i58[1], 1), 0)=TRUE>(i61[1], 0)=TRUE>(i58[1], 0)=TRUE<(i58[1], i3[1])=TRUELOAD716ARR1(java.lang.Object(ARRAY(i3[1], a481data[1])), i58[1], i61[1], java.lang.Object(java.lang.String(i91[1], i90[1], i92[1], a610[1])))≥NonInfC∧LOAD716ARR1(java.lang.Object(ARRAY(i3[1], a481data[1])), i58[1], i61[1], java.lang.Object(java.lang.String(i91[1], i90[1], i92[1], a610[1])))≥COND_LOAD716ARR1(&&(&&(&&(>(i58[1], 0), <(i58[1], i3[1])), >(i61[1], 0)), >(+(i58[1], 1), 0)), java.lang.Object(ARRAY(i3[1], a481data[1])), i58[1], i61[1], java.lang.Object(java.lang.String(i91[1], i90[1], i92[1], a610[1])))∧(UIncreasing(COND_LOAD716ARR1(&&(&&(&&(>(i58[1], 0), <(i58[1], i3[1])), >(i61[1], 0)), >(+(i58[1], 1), 0)), java.lang.Object(ARRAY(i3[1], a481data[1])), i58[1], i61[1], java.lang.Object(java.lang.String(i91[1], i90[1], i92[1], a610[1])))), ≥))

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

(8)    (i58[1] ≥ 0∧i61[1] + [-1] ≥ 0∧i58[1] + [-1] ≥ 0∧i3[1] + [-1] + [-1]i58[1] ≥ 0 ⇒ (UIncreasing(COND_LOAD716ARR1(&&(&&(&&(>(i58[1], 0), <(i58[1], i3[1])), >(i61[1], 0)), >(+(i58[1], 1), 0)), java.lang.Object(ARRAY(i3[1], a481data[1])), i58[1], i61[1], java.lang.Object(java.lang.String(i91[1], i90[1], i92[1], a610[1])))), ≥)∧[(2)bni_18 + (-1)Bound*bni_18] + [bni_18]i61[1] + [(-1)bni_18]i58[1] + [bni_18]i3[1] ≥ 0∧[(-1)bso_19] ≥ 0)

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

(9)    (i58[1] ≥ 0∧i61[1] + [-1] ≥ 0∧i58[1] + [-1] ≥ 0∧i3[1] + [-1] + [-1]i58[1] ≥ 0 ⇒ (UIncreasing(COND_LOAD716ARR1(&&(&&(&&(>(i58[1], 0), <(i58[1], i3[1])), >(i61[1], 0)), >(+(i58[1], 1), 0)), java.lang.Object(ARRAY(i3[1], a481data[1])), i58[1], i61[1], java.lang.Object(java.lang.String(i91[1], i90[1], i92[1], a610[1])))), ≥)∧[(2)bni_18 + (-1)Bound*bni_18] + [bni_18]i61[1] + [(-1)bni_18]i58[1] + [bni_18]i3[1] ≥ 0∧[(-1)bso_19] ≥ 0)

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

(10)    (i58[1] ≥ 0∧i61[1] + [-1] ≥ 0∧i58[1] + [-1] ≥ 0∧i3[1] + [-1] + [-1]i58[1] ≥ 0 ⇒ (UIncreasing(COND_LOAD716ARR1(&&(&&(&&(>(i58[1], 0), <(i58[1], i3[1])), >(i61[1], 0)), >(+(i58[1], 1), 0)), java.lang.Object(ARRAY(i3[1], a481data[1])), i58[1], i61[1], java.lang.Object(java.lang.String(i91[1], i90[1], i92[1], a610[1])))), ≥)∧[(2)bni_18 + (-1)Bound*bni_18] + [bni_18]i61[1] + [(-1)bni_18]i58[1] + [bni_18]i3[1] ≥ 0∧[(-1)bso_19] ≥ 0)

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

(11)    (i58[1] ≥ 0∧i61[1] + [-1] ≥ 0∧i58[1] + [-1] ≥ 0∧i3[1] + [-1] + [-1]i58[1] ≥ 0 ⇒ (UIncreasing(COND_LOAD716ARR1(&&(&&(&&(>(i58[1], 0), <(i58[1], i3[1])), >(i61[1], 0)), >(+(i58[1], 1), 0)), java.lang.Object(ARRAY(i3[1], a481data[1])), i58[1], i61[1], java.lang.Object(java.lang.String(i91[1], i90[1], i92[1], a610[1])))), ≥)∧0 = 0∧[(2)bni_18 + (-1)Bound*bni_18] + [bni_18]i61[1] + [(-1)bni_18]i58[1] + [bni_18]i3[1] ≥ 0∧0 = 0∧[(-1)bso_19] ≥ 0)

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

(12)    ([1] + i58[1] ≥ 0∧i61[1] + [-1] ≥ 0∧i58[1] ≥ 0∧i3[1] + [-2] + [-1]i58[1] ≥ 0 ⇒ (UIncreasing(COND_LOAD716ARR1(&&(&&(&&(>(i58[1], 0), <(i58[1], i3[1])), >(i61[1], 0)), >(+(i58[1], 1), 0)), java.lang.Object(ARRAY(i3[1], a481data[1])), i58[1], i61[1], java.lang.Object(java.lang.String(i91[1], i90[1], i92[1], a610[1])))), ≥)∧0 = 0∧[bni_18 + (-1)Bound*bni_18] + [bni_18]i61[1] + [(-1)bni_18]i58[1] + [bni_18]i3[1] ≥ 0∧0 = 0∧[(-1)bso_19] ≥ 0)

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

(13)    ([1] + i58[1] ≥ 0∧i61[1] ≥ 0∧i58[1] ≥ 0∧i3[1] + [-2] + [-1]i58[1] ≥ 0 ⇒ (UIncreasing(COND_LOAD716ARR1(&&(&&(&&(>(i58[1], 0), <(i58[1], i3[1])), >(i61[1], 0)), >(+(i58[1], 1), 0)), java.lang.Object(ARRAY(i3[1], a481data[1])), i58[1], i61[1], java.lang.Object(java.lang.String(i91[1], i90[1], i92[1], a610[1])))), ≥)∧0 = 0∧[(2)bni_18 + (-1)Bound*bni_18] + [bni_18]i61[1] + [(-1)bni_18]i58[1] + [bni_18]i3[1] ≥ 0∧0 = 0∧[(-1)bso_19] ≥ 0)

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

(14)    ([1] + i58[1] ≥ 0∧i61[1] ≥ 0∧i58[1] ≥ 0∧i3[1] ≥ 0 ⇒ (UIncreasing(COND_LOAD716ARR1(&&(&&(&&(>(i58[1], 0), <(i58[1], i3[1])), >(i61[1], 0)), >(+(i58[1], 1), 0)), java.lang.Object(ARRAY(i3[1], a481data[1])), i58[1], i61[1], java.lang.Object(java.lang.String(i91[1], i90[1], i92[1], a610[1])))), ≥)∧0 = 0∧[(4)bni_18 + (-1)Bound*bni_18] + [bni_18]i61[1] + [bni_18]i3[1] ≥ 0∧0 = 0∧[(-1)bso_19] ≥ 0)

For Pair COND_LOAD716ARR1(TRUE, java.lang.Object(ARRAY(i3, a481data)), i58, i61, java.lang.Object(java.lang.String(i91, i90, i92, a610))) → LOAD716(java.lang.Object(ARRAY(i3, a481data)), +(i58, 1), +(i61, -1)) the following chains were created:
• We consider the chain COND_LOAD716ARR1(TRUE, java.lang.Object(ARRAY(i3[2], a481data[2])), i58[2], i61[2], java.lang.Object(java.lang.String(i91[2], i90[2], i92[2], a610[2]))) → LOAD716(java.lang.Object(ARRAY(i3[2], a481data[2])), +(i58[2], 1), +(i61[2], -1)) which results in the following constraint:

(15)    (COND_LOAD716ARR1(TRUE, java.lang.Object(ARRAY(i3[2], a481data[2])), i58[2], i61[2], java.lang.Object(java.lang.String(i91[2], i90[2], i92[2], a610[2])))≥NonInfC∧COND_LOAD716ARR1(TRUE, java.lang.Object(ARRAY(i3[2], a481data[2])), i58[2], i61[2], java.lang.Object(java.lang.String(i91[2], i90[2], i92[2], a610[2])))≥LOAD716(java.lang.Object(ARRAY(i3[2], a481data[2])), +(i58[2], 1), +(i61[2], -1))∧(UIncreasing(LOAD716(java.lang.Object(ARRAY(i3[2], a481data[2])), +(i58[2], 1), +(i61[2], -1))), ≥))

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

(16)    ((UIncreasing(LOAD716(java.lang.Object(ARRAY(i3[2], a481data[2])), +(i58[2], 1), +(i61[2], -1))), ≥)∧[2 + (-1)bso_21] ≥ 0)

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

(17)    ((UIncreasing(LOAD716(java.lang.Object(ARRAY(i3[2], a481data[2])), +(i58[2], 1), +(i61[2], -1))), ≥)∧[2 + (-1)bso_21] ≥ 0)

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

(18)    ((UIncreasing(LOAD716(java.lang.Object(ARRAY(i3[2], a481data[2])), +(i58[2], 1), +(i61[2], -1))), ≥)∧[2 + (-1)bso_21] ≥ 0)

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

(19)    ((UIncreasing(LOAD716(java.lang.Object(ARRAY(i3[2], a481data[2])), +(i58[2], 1), +(i61[2], -1))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[2 + (-1)bso_21] ≥ 0)

To summarize, we get the following constraints P for the following pairs.
• LOAD716(java.lang.Object(ARRAY(i3, a481data)), i58, i61) → LOAD716ARR1(java.lang.Object(ARRAY(i3, a481data)), i58, i61, java.lang.Object(java.lang.String(i91, i90, i92, a610)))
• ((UIncreasing(LOAD716ARR1(java.lang.Object(ARRAY(i3[0], a481data[0])), i58[0], i61[0], java.lang.Object(java.lang.String(i91[0], i90[0], i92[0], a610[0])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_17] ≥ 0)

• LOAD716ARR1(java.lang.Object(ARRAY(i3, a481data)), i58, i61, java.lang.Object(java.lang.String(i91, i90, i92, a610))) → COND_LOAD716ARR1(&&(&&(&&(>(i58, 0), <(i58, i3)), >(i61, 0)), >(+(i58, 1), 0)), java.lang.Object(ARRAY(i3, a481data)), i58, i61, java.lang.Object(java.lang.String(i91, i90, i92, a610)))
• ([1] + i58[1] ≥ 0∧i61[1] ≥ 0∧i58[1] ≥ 0∧i3[1] ≥ 0 ⇒ (UIncreasing(COND_LOAD716ARR1(&&(&&(&&(>(i58[1], 0), <(i58[1], i3[1])), >(i61[1], 0)), >(+(i58[1], 1), 0)), java.lang.Object(ARRAY(i3[1], a481data[1])), i58[1], i61[1], java.lang.Object(java.lang.String(i91[1], i90[1], i92[1], a610[1])))), ≥)∧0 = 0∧[(4)bni_18 + (-1)Bound*bni_18] + [bni_18]i61[1] + [bni_18]i3[1] ≥ 0∧0 = 0∧[(-1)bso_19] ≥ 0)

• COND_LOAD716ARR1(TRUE, java.lang.Object(ARRAY(i3, a481data)), i58, i61, java.lang.Object(java.lang.String(i91, i90, i92, a610))) → LOAD716(java.lang.Object(ARRAY(i3, a481data)), +(i58, 1), +(i61, -1))
• ((UIncreasing(LOAD716(java.lang.Object(ARRAY(i3[2], a481data[2])), +(i58[2], 1), +(i61[2], -1))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[2 + (-1)bso_21] ≥ 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(LOAD716(x1, x2, x3)) = [1] + x3 + [-1]x2 + [-1]x1
POL(java.lang.Object(x1)) = x1
POL(ARRAY(x1, x2)) = [-1] + [-1]x1
POL(LOAD716ARR1(x1, x2, x3, x4)) = [1] + x3 + [-1]x2 + [-1]x1
POL(java.lang.String(x1, x2, x3, x4)) = [-1]
POL(COND_LOAD716ARR1(x1, x2, x3, x4, x5)) = [1] + x4 + [-1]x3 + [-1]x2
POL(&&(x1, x2)) = [-1]
POL(>(x1, x2)) = [-1]
POL(0) = 0
POL(<(x1, x2)) = [-1]
POL(+(x1, x2)) = x1 + x2
POL(1) = [1]
POL(-1) = [-1]

The following pairs are in P>:

COND_LOAD716ARR1(TRUE, java.lang.Object(ARRAY(i3[2], a481data[2])), i58[2], i61[2], java.lang.Object(java.lang.String(i91[2], i90[2], i92[2], a610[2]))) → LOAD716(java.lang.Object(ARRAY(i3[2], a481data[2])), +(i58[2], 1), +(i61[2], -1))

The following pairs are in Pbound:

LOAD716ARR1(java.lang.Object(ARRAY(i3[1], a481data[1])), i58[1], i61[1], java.lang.Object(java.lang.String(i91[1], i90[1], i92[1], a610[1]))) → COND_LOAD716ARR1(&&(&&(&&(>(i58[1], 0), <(i58[1], i3[1])), >(i61[1], 0)), >(+(i58[1], 1), 0)), java.lang.Object(ARRAY(i3[1], a481data[1])), i58[1], i61[1], java.lang.Object(java.lang.String(i91[1], i90[1], i92[1], a610[1])))

The following pairs are in P:

LOAD716(java.lang.Object(ARRAY(i3[0], a481data[0])), i58[0], i61[0]) → LOAD716ARR1(java.lang.Object(ARRAY(i3[0], a481data[0])), i58[0], i61[0], java.lang.Object(java.lang.String(i91[0], i90[0], i92[0], a610[0])))
LOAD716ARR1(java.lang.Object(ARRAY(i3[1], a481data[1])), i58[1], i61[1], java.lang.Object(java.lang.String(i91[1], i90[1], i92[1], a610[1]))) → COND_LOAD716ARR1(&&(&&(&&(>(i58[1], 0), <(i58[1], i3[1])), >(i61[1], 0)), >(+(i58[1], 1), 0)), java.lang.Object(ARRAY(i3[1], a481data[1])), i58[1], i61[1], java.lang.Object(java.lang.String(i91[1], i90[1], i92[1], a610[1])))

There are no usable rules.

### (33) Obligation:

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

The following domains are used:

Boolean, Integer

R is empty.

The integer pair graph contains the following rules and edges:
(0): LOAD716(java.lang.Object(ARRAY(i3[0], a481data[0])), i58[0], i61[0]) → LOAD716ARR1(java.lang.Object(ARRAY(i3[0], a481data[0])), i58[0], i61[0], java.lang.Object(java.lang.String(i91[0], i90[0], i92[0], a610[0])))
(1): LOAD716ARR1(java.lang.Object(ARRAY(i3[1], a481data[1])), i58[1], i61[1], java.lang.Object(java.lang.String(i91[1], i90[1], i92[1], a610[1]))) → COND_LOAD716ARR1(i58[1] > 0 && i58[1] < i3[1] && i61[1] > 0 && i58[1] + 1 > 0, java.lang.Object(ARRAY(i3[1], a481data[1])), i58[1], i61[1], java.lang.Object(java.lang.String(i91[1], i90[1], i92[1], a610[1])))

(0) -> (1), if (((i91[0]* i91[1])∧(i90[0]* i90[1])∧(i92[0]* i92[1])∧(a610[0]* a610[1]))∧(i58[0]* i58[1])∧(i61[0]* i61[1])∧((i3[0]* i3[1])∧(a481data[0]* a481data[1])))

The set Q consists of the following terms:
Load716ARR1(java.lang.Object(ARRAY(x0, x1)), x2, x3, java.lang.Object(java.lang.String(x4, x5, x6, x7)))
Cond_Load716ARR1(TRUE, java.lang.Object(ARRAY(x0, x1)), x2, x3, java.lang.Object(java.lang.String(x4, x5, x6, x7)))

### (34) IDependencyGraphProof (EQUIVALENT transformation)

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

### (36) Obligation:

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

The following domains are used:

Integer

R is empty.

The integer pair graph contains the following rules and edges:
(0): LOAD716(java.lang.Object(ARRAY(i3[0], a481data[0])), i58[0], i61[0]) → LOAD716ARR1(java.lang.Object(ARRAY(i3[0], a481data[0])), i58[0], i61[0], java.lang.Object(java.lang.String(i91[0], i90[0], i92[0], a610[0])))
(2): COND_LOAD716ARR1(TRUE, java.lang.Object(ARRAY(i3[2], a481data[2])), i58[2], i61[2], java.lang.Object(java.lang.String(i91[2], i90[2], i92[2], a610[2]))) → LOAD716(java.lang.Object(ARRAY(i3[2], a481data[2])), i58[2] + 1, i61[2] + -1)

(2) -> (0), if (((i3[2]* i3[0])∧(a481data[2]* a481data[0]))∧(i61[2] + -1* i61[0])∧(i58[2] + 1* i58[0]))

The set Q consists of the following terms: