Termination proof of /tmp/tmpF6eH5p/IntRTA.jar

Termination of the given JBC could be proven:

0 JBC

↳1 JBC2FIG (⇐)

↳2 FIGraph

↳3 FIGtoITRSProof (⇐)

↳4 ITRS

↳5 DuplicateArgsRemoverProof (⇔)

↳6 ITRS

↳7 ITRStoIDPProof (⇔)

↳8 IDP

↳9 UsableRulesProof (⇔)

↳10 IDP

↳11 ItpfGraphProof (⇔)

↳12 IDP

↳13 IDPNonInfProof (⇐)

↳14 AND

    ↳15 IDP

        ↳16 IDependencyGraphProof (⇔)

        ↳17 TRUE

    ↳18 IDP

        ↳19 IDependencyGraphProof (⇔)

        ↳20 TRUE

(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:
Load593(java.lang.Object(IntRTA(x0)), java.lang.Object(IntRTA(x1)), java.lang.Object(IntRTA(x0)))
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:

Load593(x1, x2, x3) → Load593(x2, x3)
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:
Load593(java.lang.Object(IntRTA(x0)), java.lang.Object(IntRTA(x1)))
Cond_Load593(TRUE, java.lang.Object(IntRTA(x0)), java.lang.Object(IntRTA(x1)))

(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:
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:
Load593(java.lang.Object(IntRTA(x0)), java.lang.Object(IntRTA(x1)))
Cond_Load593(TRUE, java.lang.Object(IntRTA(x0)), java.lang.Object(IntRTA(x1)))

(9) UsableRulesProof (EQUIVALENT transformation)

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

(10) Obligation:

IDP problem:
The following function symbols are pre-defined:

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

The following domains are used:

Boolean, Integer

R is empty.

The integer pair graph contains the following rules and edges:
(0): 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)))

(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:
Load593(java.lang.Object(IntRTA(x0)), java.lang.Object(IntRTA(x1)))
Cond_Load593(TRUE, java.lang.Object(IntRTA(x0)), java.lang.Object(IntRTA(x1)))

(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

(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:
Load593(java.lang.Object(IntRTA(x0)), java.lang.Object(IntRTA(x1)))
Cond_Load593(TRUE, java.lang.Object(IntRTA(x0)), java.lang.Object(IntRTA(x1)))

(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))=TRUE ⇒ LOAD593(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])))∧(U^Increasing(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])=TRUE ⇒ LOAD593(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])))∧(U^Increasing(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 ⇒ (U^Increasing(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 ⇒ (U^Increasing(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 ⇒ (U^Increasing(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 ⇒ (U^Increasing(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:
(7)    (COND_LOAD593(TRUE, java.lang.Object(IntRTA(i38[1])), java.lang.Object(IntRTA(i13[1])))≥NonInfC∧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))))∧(U^Increasing(LOAD593(java.lang.Object(IntRTA(i38[1])), java.lang.Object(IntRTA(+(i13[1], 1))))), ≥))

We simplified constraint (7) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(8)    ((U^Increasing(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)    ((U^Increasing(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)    ((U^Increasing(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)    ((U^Increasing(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 ⇒ (U^Increasing(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))))
- ((U^Increasing(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 P_bound 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 P_bound.
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 P_bound:

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.

(14) Complex Obligation (AND)

(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:
Load593(java.lang.Object(IntRTA(x0)), java.lang.Object(IntRTA(x1)))
Cond_Load593(TRUE, java.lang.Object(IntRTA(x0)), java.lang.Object(IntRTA(x1)))

(16) IDependencyGraphProof (EQUIVALENT transformation)

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

(17) TRUE

(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:
Load593(java.lang.Object(IntRTA(x0)), java.lang.Object(IntRTA(x1)))
Cond_Load593(TRUE, java.lang.Object(IntRTA(x0)), java.lang.Object(IntRTA(x1)))

(19) IDependencyGraphProof (EQUIVALENT transformation)

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

(0) Obligation:

(1) JBC2FIG (SOUND transformation)

(2) Obligation:

(3) FIGtoITRSProof (SOUND transformation)

(4) Obligation:

(5) DuplicateArgsRemoverProof (EQUIVALENT transformation)

(6) Obligation:

(7) ITRStoIDPProof (EQUIVALENT transformation)

(8) Obligation:

(9) UsableRulesProof (EQUIVALENT transformation)

(10) Obligation:

(11) ItpfGraphProof (EQUIVALENT transformation)

(12) Obligation:

(13) IDPNonInfProof (SOUND transformation)

(14) Complex Obligation (AND)

(15) Obligation:

(16) IDependencyGraphProof (EQUIVALENT transformation)

(17) TRUE

(18) Obligation:

(19) IDependencyGraphProof (EQUIVALENT transformation)

(20) TRUE