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 IDPNonInfProof (⇐)
↳12 AND
    ↳13 IDP
        ↳14 IDependencyGraphProof (⇔)
        ↳15 TRUE
    ↳16 IDP
        ↳17 IDependencyGraphProof (⇔)
        ↳18 TRUE

(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: DivMinus

(1) JBC2FIG (SOUND transformation)

Constructed FIGraph.

(2) Obligation:

FIGraph based on JBC Program:
Graph of 182 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:
Load707(i55, i51, i55, i53) → Cond_Load707(i55 > 0 && i51 >= i55, i55, i51, i55, i53)
Cond_Load707(TRUE, i55, i51, i55, i53) → Load707(i55, i51 - i55, i55, i53 + 1)
The set Q consists of the following terms:
Load707(x0, x1, x0, x2)
Cond_Load707(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:

Load707(x1, x2, x3, x4) → Load707(x2, x3, x4)
Cond_Load707(x1, x2, x3, x4, x5) → Cond_Load707(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:
Load707(i51, i55, i53) → Cond_Load707(i55 > 0 && i51 >= i55, i51, i55, i53)
Cond_Load707(TRUE, i51, i55, i53) → Load707(i51 - i55, i55, i53 + 1)
The set Q consists of the following terms:
Load707(x0, x1, x2)
Cond_Load707(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:
Load707(i51, i55, i53) → Cond_Load707(i55 > 0 && i51 >= i55, i51, i55, i53)
Cond_Load707(TRUE, i51, i55, i53) → Load707(i51 - i55, i55, i53 + 1)

The integer pair graph contains the following rules and edges:
(0): LOAD707(i51[0], i55[0], i53[0]) → COND_LOAD707(i55[0] > 0 && i51[0] >= i55[0], i51[0], i55[0], i53[0])
(1): COND_LOAD707(TRUE, i51[1], i55[1], i53[1]) → LOAD707(i51[1] - i55[1], i55[1], i53[1] + 1)

(0) -> (1), if ((i51[0] →* i51[1])∧(i55[0] →* i55[1])∧(i55[0] > 0 && i51[0] >= i55[0] →* TRUE)∧(i53[0] →* i53[1]))


(1) -> (0), if ((i51[1] - i55[1] →* i51[0])∧(i53[1] + 1 →* i53[0])∧(i55[1] →* i55[0]))



The set Q consists of the following terms:
Load707(x0, x1, x2)
Cond_Load707(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): LOAD707(i51[0], i55[0], i53[0]) → COND_LOAD707(i55[0] > 0 && i51[0] >= i55[0], i51[0], i55[0], i53[0])
(1): COND_LOAD707(TRUE, i51[1], i55[1], i53[1]) → LOAD707(i51[1] - i55[1], i55[1], i53[1] + 1)

(0) -> (1), if ((i51[0] →* i51[1])∧(i55[0] →* i55[1])∧(i55[0] > 0 && i51[0] >= i55[0] →* TRUE)∧(i53[0] →* i53[1]))


(1) -> (0), if ((i51[1] - i55[1] →* i51[0])∧(i53[1] + 1 →* i53[0])∧(i55[1] →* i55[0]))



The set Q consists of the following terms:
Load707(x0, x1, x2)
Cond_Load707(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 LOAD707(i51, i55, i53) → COND_LOAD707(&&(>(i55, 0), >=(i51, i55)), i51, i55, i53) the following chains were created:
  • We consider the chain LOAD707(i51[0], i55[0], i53[0]) → COND_LOAD707(&&(>(i55[0], 0), >=(i51[0], i55[0])), i51[0], i55[0], i53[0]), COND_LOAD707(TRUE, i51[1], i55[1], i53[1]) → LOAD707(-(i51[1], i55[1]), i55[1], +(i53[1], 1)) which results in the following constraint:

    (1)    (i51[0]=i51[1]∧i55[0]=i55[1]∧&&(>(i55[0], 0), >=(i51[0], i55[0]))=TRUE∧i53[0]=i53[1] ⇒ LOAD707(i51[0], i55[0], i53[0])≥NonInfC∧LOAD707(i51[0], i55[0], i53[0])≥COND_LOAD707(&&(>(i55[0], 0), >=(i51[0], i55[0])), i51[0], i55[0], i53[0])∧(UIncreasing(COND_LOAD707(&&(>(i55[0], 0), >=(i51[0], i55[0])), i51[0], i55[0], i53[0])), ≥))



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

    (2)    (>(i55[0], 0)=TRUE∧>=(i51[0], i55[0])=TRUE ⇒ LOAD707(i51[0], i55[0], i53[0])≥NonInfC∧LOAD707(i51[0], i55[0], i53[0])≥COND_LOAD707(&&(>(i55[0], 0), >=(i51[0], i55[0])), i51[0], i55[0], i53[0])∧(UIncreasing(COND_LOAD707(&&(>(i55[0], 0), >=(i51[0], i55[0])), i51[0], i55[0], i53[0])), ≥))



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

    (3)    (i55[0] + [-1] ≥ 0∧i51[0] + [-1]i55[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD707(&&(>(i55[0], 0), >=(i51[0], i55[0])), i51[0], i55[0], i53[0])), ≥)∧[(-1)bni_15 + (-1)Bound*bni_15] + [(-1)bni_15]i55[0] + [bni_15]i51[0] ≥ 0∧[(-1)bso_16] ≥ 0)



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

    (4)    (i55[0] + [-1] ≥ 0∧i51[0] + [-1]i55[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD707(&&(>(i55[0], 0), >=(i51[0], i55[0])), i51[0], i55[0], i53[0])), ≥)∧[(-1)bni_15 + (-1)Bound*bni_15] + [(-1)bni_15]i55[0] + [bni_15]i51[0] ≥ 0∧[(-1)bso_16] ≥ 0)



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

    (5)    (i55[0] + [-1] ≥ 0∧i51[0] + [-1]i55[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD707(&&(>(i55[0], 0), >=(i51[0], i55[0])), i51[0], i55[0], i53[0])), ≥)∧[(-1)bni_15 + (-1)Bound*bni_15] + [(-1)bni_15]i55[0] + [bni_15]i51[0] ≥ 0∧[(-1)bso_16] ≥ 0)



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

    (6)    (i55[0] + [-1] ≥ 0∧i51[0] + [-1]i55[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD707(&&(>(i55[0], 0), >=(i51[0], i55[0])), i51[0], i55[0], i53[0])), ≥)∧0 = 0∧[(-1)bni_15 + (-1)Bound*bni_15] + [(-1)bni_15]i55[0] + [bni_15]i51[0] ≥ 0∧0 = 0∧[(-1)bso_16] ≥ 0)



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

    (7)    (i55[0] ≥ 0∧i51[0] + [-1] + [-1]i55[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD707(&&(>(i55[0], 0), >=(i51[0], i55[0])), i51[0], i55[0], i53[0])), ≥)∧0 = 0∧[(-2)bni_15 + (-1)Bound*bni_15] + [(-1)bni_15]i55[0] + [bni_15]i51[0] ≥ 0∧0 = 0∧[(-1)bso_16] ≥ 0)



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

    (8)    (i55[0] ≥ 0∧i51[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD707(&&(>(i55[0], 0), >=(i51[0], i55[0])), i51[0], i55[0], i53[0])), ≥)∧0 = 0∧[(-1)bni_15 + (-1)Bound*bni_15] + [bni_15]i51[0] ≥ 0∧0 = 0∧[(-1)bso_16] ≥ 0)







For Pair COND_LOAD707(TRUE, i51, i55, i53) → LOAD707(-(i51, i55), i55, +(i53, 1)) the following chains were created:
  • We consider the chain LOAD707(i51[0], i55[0], i53[0]) → COND_LOAD707(&&(>(i55[0], 0), >=(i51[0], i55[0])), i51[0], i55[0], i53[0]), COND_LOAD707(TRUE, i51[1], i55[1], i53[1]) → LOAD707(-(i51[1], i55[1]), i55[1], +(i53[1], 1)), LOAD707(i51[0], i55[0], i53[0]) → COND_LOAD707(&&(>(i55[0], 0), >=(i51[0], i55[0])), i51[0], i55[0], i53[0]) which results in the following constraint:

    (9)    (i51[0]=i51[1]∧i55[0]=i55[1]∧&&(>(i55[0], 0), >=(i51[0], i55[0]))=TRUE∧i53[0]=i53[1]∧-(i51[1], i55[1])=i51[0]1∧+(i53[1], 1)=i53[0]1∧i55[1]=i55[0]1 ⇒ COND_LOAD707(TRUE, i51[1], i55[1], i53[1])≥NonInfC∧COND_LOAD707(TRUE, i51[1], i55[1], i53[1])≥LOAD707(-(i51[1], i55[1]), i55[1], +(i53[1], 1))∧(UIncreasing(LOAD707(-(i51[1], i55[1]), i55[1], +(i53[1], 1))), ≥))



    We simplified constraint (9) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (10)    (>(i55[0], 0)=TRUE∧>=(i51[0], i55[0])=TRUE ⇒ COND_LOAD707(TRUE, i51[0], i55[0], i53[0])≥NonInfC∧COND_LOAD707(TRUE, i51[0], i55[0], i53[0])≥LOAD707(-(i51[0], i55[0]), i55[0], +(i53[0], 1))∧(UIncreasing(LOAD707(-(i51[1], i55[1]), i55[1], +(i53[1], 1))), ≥))



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

    (11)    (i55[0] + [-1] ≥ 0∧i51[0] + [-1]i55[0] ≥ 0 ⇒ (UIncreasing(LOAD707(-(i51[1], i55[1]), i55[1], +(i53[1], 1))), ≥)∧[(-1)bni_17 + (-1)Bound*bni_17] + [(-1)bni_17]i55[0] + [bni_17]i51[0] ≥ 0∧[(-1)bso_18] + i55[0] ≥ 0)



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

    (12)    (i55[0] + [-1] ≥ 0∧i51[0] + [-1]i55[0] ≥ 0 ⇒ (UIncreasing(LOAD707(-(i51[1], i55[1]), i55[1], +(i53[1], 1))), ≥)∧[(-1)bni_17 + (-1)Bound*bni_17] + [(-1)bni_17]i55[0] + [bni_17]i51[0] ≥ 0∧[(-1)bso_18] + i55[0] ≥ 0)



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

    (13)    (i55[0] + [-1] ≥ 0∧i51[0] + [-1]i55[0] ≥ 0 ⇒ (UIncreasing(LOAD707(-(i51[1], i55[1]), i55[1], +(i53[1], 1))), ≥)∧[(-1)bni_17 + (-1)Bound*bni_17] + [(-1)bni_17]i55[0] + [bni_17]i51[0] ≥ 0∧[(-1)bso_18] + i55[0] ≥ 0)



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

    (14)    (i55[0] + [-1] ≥ 0∧i51[0] + [-1]i55[0] ≥ 0 ⇒ (UIncreasing(LOAD707(-(i51[1], i55[1]), i55[1], +(i53[1], 1))), ≥)∧0 = 0∧[(-1)bni_17 + (-1)Bound*bni_17] + [(-1)bni_17]i55[0] + [bni_17]i51[0] ≥ 0∧0 = 0∧[(-1)bso_18] + i55[0] ≥ 0)



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

    (15)    (i55[0] ≥ 0∧i51[0] + [-1] + [-1]i55[0] ≥ 0 ⇒ (UIncreasing(LOAD707(-(i51[1], i55[1]), i55[1], +(i53[1], 1))), ≥)∧0 = 0∧[(-2)bni_17 + (-1)Bound*bni_17] + [(-1)bni_17]i55[0] + [bni_17]i51[0] ≥ 0∧0 = 0∧[1 + (-1)bso_18] + i55[0] ≥ 0)



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

    (16)    (i55[0] ≥ 0∧i51[0] ≥ 0 ⇒ (UIncreasing(LOAD707(-(i51[1], i55[1]), i55[1], +(i53[1], 1))), ≥)∧0 = 0∧[(-1)bni_17 + (-1)Bound*bni_17] + [bni_17]i51[0] ≥ 0∧0 = 0∧[1 + (-1)bso_18] + i55[0] ≥ 0)







To summarize, we get the following constraints P≥ for the following pairs.
  • LOAD707(i51, i55, i53) → COND_LOAD707(&&(>(i55, 0), >=(i51, i55)), i51, i55, i53)
    • (i55[0] ≥ 0∧i51[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD707(&&(>(i55[0], 0), >=(i51[0], i55[0])), i51[0], i55[0], i53[0])), ≥)∧0 = 0∧[(-1)bni_15 + (-1)Bound*bni_15] + [bni_15]i51[0] ≥ 0∧0 = 0∧[(-1)bso_16] ≥ 0)

  • COND_LOAD707(TRUE, i51, i55, i53) → LOAD707(-(i51, i55), i55, +(i53, 1))
    • (i55[0] ≥ 0∧i51[0] ≥ 0 ⇒ (UIncreasing(LOAD707(-(i51[1], i55[1]), i55[1], +(i53[1], 1))), ≥)∧0 = 0∧[(-1)bni_17 + (-1)Bound*bni_17] + [bni_17]i51[0] ≥ 0∧0 = 0∧[1 + (-1)bso_18] + i55[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) = 0   
POL(LOAD707(x1, x2, x3)) = [-1] + [-1]x2 + x1   
POL(COND_LOAD707(x1, x2, x3, x4)) = [-1] + [-1]x3 + x2 + [-1]x1   
POL(&&(x1, x2)) = 0   
POL(>(x1, x2)) = [-1]   
POL(0) = 0   
POL(>=(x1, x2)) = [-1]   
POL(-(x1, x2)) = x1 + [-1]x2   
POL(+(x1, x2)) = x1 + x2   
POL(1) = [1]   

The following pairs are in P>:

COND_LOAD707(TRUE, i51[1], i55[1], i53[1]) → LOAD707(-(i51[1], i55[1]), i55[1], +(i53[1], 1))

The following pairs are in Pbound:

LOAD707(i51[0], i55[0], i53[0]) → COND_LOAD707(&&(>(i55[0], 0), >=(i51[0], i55[0])), i51[0], i55[0], i53[0])
COND_LOAD707(TRUE, i51[1], i55[1], i53[1]) → LOAD707(-(i51[1], i55[1]), i55[1], +(i53[1], 1))

The following pairs are in P≥:

LOAD707(i51[0], i55[0], i53[0]) → COND_LOAD707(&&(>(i55[0], 0), >=(i51[0], i55[0])), i51[0], i55[0], i53[0])

At least the following rules have been oriented under context sensitive arithmetic replacement:

&&(TRUE, TRUE)1 ↔ TRUE1
&&(TRUE, FALSE)1 ↔ FALSE1
&&(FALSE, TRUE)1 ↔ FALSE1
&&(FALSE, FALSE)1 ↔ FALSE1

(12) Complex Obligation (AND)

(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): LOAD707(i51[0], i55[0], i53[0]) → COND_LOAD707(i55[0] > 0 && i51[0] >= i55[0], i51[0], i55[0], i53[0])


The set Q consists of the following terms:
Load707(x0, x1, x2)
Cond_Load707(TRUE, x0, x1, x2)

(14) IDependencyGraphProof (EQUIVALENT transformation)

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

(15) TRUE

(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:
Load707(x0, x1, x2)
Cond_Load707(TRUE, x0, x1, x2)

(17) IDependencyGraphProof (EQUIVALENT transformation)

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

(18) TRUE