Termination of the given JBC could be proven:

0 JBC
↳1 JBC2FIG (⇐)
↳2 FIGraph
↳3 FIGtoITRSProof (⇐)
↳4 ITRS
↳5 ITRStoIDPProof (⇔)
↳6 IDP
↳7 UsableRulesProof (⇔)
↳8 IDP
↳9 IDPNonInfProof (⇐)
↳10 AND
    ↳11 IDP
        ↳12 IDependencyGraphProof (⇔)
        ↳13 IDP
        ↳14 IDPNonInfProof (⇐)
        ↳15 AND
            ↳16 IDP
                ↳17 IDependencyGraphProof (⇔)
                ↳18 TRUE
            ↳19 IDP
                ↳20 IDependencyGraphProof (⇔)
                ↳21 TRUE
    ↳22 IDP
        ↳23 IDependencyGraphProof (⇔)
        ↳24 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: PastaA1

(1) JBC2FIG (SOUND transformation)

Constructed FIGraph.

(2) Obligation:

FIGraph based on JBC Program:
Graph of 110 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:
Load139(i15) → Cond_Load139(i15 > 0, i15)
Cond_Load139(TRUE, i15) → Load274(i15, 0)
Load274(i15, i21) → Cond_Load274(i21 >= 0 && i21 < i15 && i21 + 1 > 0, i15, i21)
Cond_Load274(TRUE, i15, i21) → Load274(i15, i21 + 1)
Load274(i15, i21) → Cond_Load2741(i15 > 0 && i21 >= i15, i15, i21)
Cond_Load2741(TRUE, i15, i21) → Load139(i15 + -1)
The set Q consists of the following terms:
Load139(x0)
Cond_Load139(TRUE, x0)
Load274(x0, x1)
Cond_Load274(TRUE, x0, x1)
Cond_Load2741(TRUE, x0, x1)

(5) ITRStoIDPProof (EQUIVALENT transformation)

Added dependency pairs

(6) 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, Boolean


The ITRS R consists of the following rules:
Load139(i15) → Cond_Load139(i15 > 0, i15)
Cond_Load139(TRUE, i15) → Load274(i15, 0)
Load274(i15, i21) → Cond_Load274(i21 >= 0 && i21 < i15 && i21 + 1 > 0, i15, i21)
Cond_Load274(TRUE, i15, i21) → Load274(i15, i21 + 1)
Load274(i15, i21) → Cond_Load2741(i15 > 0 && i21 >= i15, i15, i21)
Cond_Load2741(TRUE, i15, i21) → Load139(i15 + -1)

The integer pair graph contains the following rules and edges:
(0): LOAD139(i15[0]) → COND_LOAD139(i15[0] > 0, i15[0])
(1): COND_LOAD139(TRUE, i15[1]) → LOAD274(i15[1], 0)
(2): LOAD274(i15[2], i21[2]) → COND_LOAD274(i21[2] >= 0 && i21[2] < i15[2] && i21[2] + 1 > 0, i15[2], i21[2])
(3): COND_LOAD274(TRUE, i15[3], i21[3]) → LOAD274(i15[3], i21[3] + 1)
(4): LOAD274(i15[4], i21[4]) → COND_LOAD2741(i15[4] > 0 && i21[4] >= i15[4], i15[4], i21[4])
(5): COND_LOAD2741(TRUE, i15[5], i21[5]) → LOAD139(i15[5] + -1)

(0) -> (1), if ((i15[0] →* i15[1])∧(i15[0] > 0 →* TRUE))


(1) -> (2), if ((0 →* i21[2])∧(i15[1] →* i15[2]))


(1) -> (4), if ((0 →* i21[4])∧(i15[1] →* i15[4]))


(2) -> (3), if ((i15[2] →* i15[3])∧(i21[2] →* i21[3])∧(i21[2] >= 0 && i21[2] < i15[2] && i21[2] + 1 > 0 →* TRUE))


(3) -> (2), if ((i21[3] + 1 →* i21[2])∧(i15[3] →* i15[2]))


(3) -> (4), if ((i21[3] + 1 →* i21[4])∧(i15[3] →* i15[4]))


(4) -> (5), if ((i15[4] > 0 && i21[4] >= i15[4] →* TRUE)∧(i15[4] →* i15[5])∧(i21[4] →* i21[5]))


(5) -> (0), if ((i15[5] + -1 →* i15[0]))



The set Q consists of the following terms:
Load139(x0)
Cond_Load139(TRUE, x0)
Load274(x0, x1)
Cond_Load274(TRUE, x0, x1)
Cond_Load2741(TRUE, x0, x1)

(7) 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.

(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:

Integer, Boolean


R is empty.

The integer pair graph contains the following rules and edges:
(0): LOAD139(i15[0]) → COND_LOAD139(i15[0] > 0, i15[0])
(1): COND_LOAD139(TRUE, i15[1]) → LOAD274(i15[1], 0)
(2): LOAD274(i15[2], i21[2]) → COND_LOAD274(i21[2] >= 0 && i21[2] < i15[2] && i21[2] + 1 > 0, i15[2], i21[2])
(3): COND_LOAD274(TRUE, i15[3], i21[3]) → LOAD274(i15[3], i21[3] + 1)
(4): LOAD274(i15[4], i21[4]) → COND_LOAD2741(i15[4] > 0 && i21[4] >= i15[4], i15[4], i21[4])
(5): COND_LOAD2741(TRUE, i15[5], i21[5]) → LOAD139(i15[5] + -1)

(0) -> (1), if ((i15[0] →* i15[1])∧(i15[0] > 0 →* TRUE))


(1) -> (2), if ((0 →* i21[2])∧(i15[1] →* i15[2]))


(1) -> (4), if ((0 →* i21[4])∧(i15[1] →* i15[4]))


(2) -> (3), if ((i15[2] →* i15[3])∧(i21[2] →* i21[3])∧(i21[2] >= 0 && i21[2] < i15[2] && i21[2] + 1 > 0 →* TRUE))


(3) -> (2), if ((i21[3] + 1 →* i21[2])∧(i15[3] →* i15[2]))


(3) -> (4), if ((i21[3] + 1 →* i21[4])∧(i15[3] →* i15[4]))


(4) -> (5), if ((i15[4] > 0 && i21[4] >= i15[4] →* TRUE)∧(i15[4] →* i15[5])∧(i21[4] →* i21[5]))


(5) -> (0), if ((i15[5] + -1 →* i15[0]))



The set Q consists of the following terms:
Load139(x0)
Cond_Load139(TRUE, x0)
Load274(x0, x1)
Cond_Load274(TRUE, x0, x1)
Cond_Load2741(TRUE, x0, x1)

(9) 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 LOAD139(i15) → COND_LOAD139(>(i15, 0), i15) the following chains were created:
  • We consider the chain LOAD139(i15[0]) → COND_LOAD139(>(i15[0], 0), i15[0]), COND_LOAD139(TRUE, i15[1]) → LOAD274(i15[1], 0) which results in the following constraint:

    (1)    (i15[0]=i15[1]∧>(i15[0], 0)=TRUE ⇒ LOAD139(i15[0])≥NonInfC∧LOAD139(i15[0])≥COND_LOAD139(>(i15[0], 0), i15[0])∧(UIncreasing(COND_LOAD139(>(i15[0], 0), i15[0])), ≥))



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

    (2)    (>(i15[0], 0)=TRUE ⇒ LOAD139(i15[0])≥NonInfC∧LOAD139(i15[0])≥COND_LOAD139(>(i15[0], 0), i15[0])∧(UIncreasing(COND_LOAD139(>(i15[0], 0), i15[0])), ≥))



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

    (3)    (i15[0] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD139(>(i15[0], 0), i15[0])), ≥)∧[(-1)bni_16 + (-1)Bound*bni_16] + [bni_16]i15[0] ≥ 0∧[(-1)bso_17] ≥ 0)



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

    (4)    (i15[0] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD139(>(i15[0], 0), i15[0])), ≥)∧[(-1)bni_16 + (-1)Bound*bni_16] + [bni_16]i15[0] ≥ 0∧[(-1)bso_17] ≥ 0)



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

    (5)    (i15[0] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD139(>(i15[0], 0), i15[0])), ≥)∧[(-1)bni_16 + (-1)Bound*bni_16] + [bni_16]i15[0] ≥ 0∧[(-1)bso_17] ≥ 0)



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

    (6)    (i15[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD139(>(i15[0], 0), i15[0])), ≥)∧[(-1)Bound*bni_16] + [bni_16]i15[0] ≥ 0∧[(-1)bso_17] ≥ 0)







For Pair COND_LOAD139(TRUE, i15) → LOAD274(i15, 0) the following chains were created:
  • We consider the chain COND_LOAD139(TRUE, i15[1]) → LOAD274(i15[1], 0) which results in the following constraint:

    (7)    (COND_LOAD139(TRUE, i15[1])≥NonInfC∧COND_LOAD139(TRUE, i15[1])≥LOAD274(i15[1], 0)∧(UIncreasing(LOAD274(i15[1], 0)), ≥))



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

    (8)    ((UIncreasing(LOAD274(i15[1], 0)), ≥)∧[(-1)bso_19] ≥ 0)



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

    (9)    ((UIncreasing(LOAD274(i15[1], 0)), ≥)∧[(-1)bso_19] ≥ 0)



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

    (10)    ((UIncreasing(LOAD274(i15[1], 0)), ≥)∧[(-1)bso_19] ≥ 0)



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

    (11)    ((UIncreasing(LOAD274(i15[1], 0)), ≥)∧0 = 0∧[(-1)bso_19] ≥ 0)







For Pair LOAD274(i15, i21) → COND_LOAD274(&&(&&(>=(i21, 0), <(i21, i15)), >(+(i21, 1), 0)), i15, i21) the following chains were created:
  • We consider the chain LOAD274(i15[2], i21[2]) → COND_LOAD274(&&(&&(>=(i21[2], 0), <(i21[2], i15[2])), >(+(i21[2], 1), 0)), i15[2], i21[2]), COND_LOAD274(TRUE, i15[3], i21[3]) → LOAD274(i15[3], +(i21[3], 1)) which results in the following constraint:

    (12)    (i15[2]=i15[3]∧i21[2]=i21[3]∧&&(&&(>=(i21[2], 0), <(i21[2], i15[2])), >(+(i21[2], 1), 0))=TRUE ⇒ LOAD274(i15[2], i21[2])≥NonInfC∧LOAD274(i15[2], i21[2])≥COND_LOAD274(&&(&&(>=(i21[2], 0), <(i21[2], i15[2])), >(+(i21[2], 1), 0)), i15[2], i21[2])∧(UIncreasing(COND_LOAD274(&&(&&(>=(i21[2], 0), <(i21[2], i15[2])), >(+(i21[2], 1), 0)), i15[2], i21[2])), ≥))



    We simplified constraint (12) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (13)    (>(+(i21[2], 1), 0)=TRUE∧>=(i21[2], 0)=TRUE∧<(i21[2], i15[2])=TRUE ⇒ LOAD274(i15[2], i21[2])≥NonInfC∧LOAD274(i15[2], i21[2])≥COND_LOAD274(&&(&&(>=(i21[2], 0), <(i21[2], i15[2])), >(+(i21[2], 1), 0)), i15[2], i21[2])∧(UIncreasing(COND_LOAD274(&&(&&(>=(i21[2], 0), <(i21[2], i15[2])), >(+(i21[2], 1), 0)), i15[2], i21[2])), ≥))



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

    (14)    (i21[2] ≥ 0∧i21[2] ≥ 0∧i15[2] + [-1] + [-1]i21[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD274(&&(&&(>=(i21[2], 0), <(i21[2], i15[2])), >(+(i21[2], 1), 0)), i15[2], i21[2])), ≥)∧[(-1)bni_20 + (-1)Bound*bni_20] + [bni_20]i15[2] ≥ 0∧[(-1)bso_21] ≥ 0)



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

    (15)    (i21[2] ≥ 0∧i21[2] ≥ 0∧i15[2] + [-1] + [-1]i21[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD274(&&(&&(>=(i21[2], 0), <(i21[2], i15[2])), >(+(i21[2], 1), 0)), i15[2], i21[2])), ≥)∧[(-1)bni_20 + (-1)Bound*bni_20] + [bni_20]i15[2] ≥ 0∧[(-1)bso_21] ≥ 0)



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

    (16)    (i21[2] ≥ 0∧i21[2] ≥ 0∧i15[2] + [-1] + [-1]i21[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD274(&&(&&(>=(i21[2], 0), <(i21[2], i15[2])), >(+(i21[2], 1), 0)), i15[2], i21[2])), ≥)∧[(-1)bni_20 + (-1)Bound*bni_20] + [bni_20]i15[2] ≥ 0∧[(-1)bso_21] ≥ 0)



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

    (17)    (i21[2] ≥ 0∧i21[2] ≥ 0∧i15[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD274(&&(&&(>=(i21[2], 0), <(i21[2], i15[2])), >(+(i21[2], 1), 0)), i15[2], i21[2])), ≥)∧[(-1)Bound*bni_20] + [bni_20]i21[2] + [bni_20]i15[2] ≥ 0∧[(-1)bso_21] ≥ 0)







For Pair COND_LOAD274(TRUE, i15, i21) → LOAD274(i15, +(i21, 1)) the following chains were created:
  • We consider the chain COND_LOAD274(TRUE, i15[3], i21[3]) → LOAD274(i15[3], +(i21[3], 1)) which results in the following constraint:

    (18)    (COND_LOAD274(TRUE, i15[3], i21[3])≥NonInfC∧COND_LOAD274(TRUE, i15[3], i21[3])≥LOAD274(i15[3], +(i21[3], 1))∧(UIncreasing(LOAD274(i15[3], +(i21[3], 1))), ≥))



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

    (19)    ((UIncreasing(LOAD274(i15[3], +(i21[3], 1))), ≥)∧[(-1)bso_23] ≥ 0)



    We simplified constraint (19) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (20)    ((UIncreasing(LOAD274(i15[3], +(i21[3], 1))), ≥)∧[(-1)bso_23] ≥ 0)



    We simplified constraint (20) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (21)    ((UIncreasing(LOAD274(i15[3], +(i21[3], 1))), ≥)∧[(-1)bso_23] ≥ 0)



    We simplified constraint (21) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

    (22)    ((UIncreasing(LOAD274(i15[3], +(i21[3], 1))), ≥)∧0 = 0∧0 = 0∧[(-1)bso_23] ≥ 0)







For Pair LOAD274(i15, i21) → COND_LOAD2741(&&(>(i15, 0), >=(i21, i15)), i15, i21) the following chains were created:
  • We consider the chain LOAD274(i15[4], i21[4]) → COND_LOAD2741(&&(>(i15[4], 0), >=(i21[4], i15[4])), i15[4], i21[4]), COND_LOAD2741(TRUE, i15[5], i21[5]) → LOAD139(+(i15[5], -1)) which results in the following constraint:

    (23)    (&&(>(i15[4], 0), >=(i21[4], i15[4]))=TRUE∧i15[4]=i15[5]∧i21[4]=i21[5] ⇒ LOAD274(i15[4], i21[4])≥NonInfC∧LOAD274(i15[4], i21[4])≥COND_LOAD2741(&&(>(i15[4], 0), >=(i21[4], i15[4])), i15[4], i21[4])∧(UIncreasing(COND_LOAD2741(&&(>(i15[4], 0), >=(i21[4], i15[4])), i15[4], i21[4])), ≥))



    We simplified constraint (23) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (24)    (>(i15[4], 0)=TRUE∧>=(i21[4], i15[4])=TRUE ⇒ LOAD274(i15[4], i21[4])≥NonInfC∧LOAD274(i15[4], i21[4])≥COND_LOAD2741(&&(>(i15[4], 0), >=(i21[4], i15[4])), i15[4], i21[4])∧(UIncreasing(COND_LOAD2741(&&(>(i15[4], 0), >=(i21[4], i15[4])), i15[4], i21[4])), ≥))



    We simplified constraint (24) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (25)    (i15[4] + [-1] ≥ 0∧i21[4] + [-1]i15[4] ≥ 0 ⇒ (UIncreasing(COND_LOAD2741(&&(>(i15[4], 0), >=(i21[4], i15[4])), i15[4], i21[4])), ≥)∧[(-1)bni_24 + (-1)Bound*bni_24] + [bni_24]i15[4] ≥ 0∧[(-1)bso_25] ≥ 0)



    We simplified constraint (25) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (26)    (i15[4] + [-1] ≥ 0∧i21[4] + [-1]i15[4] ≥ 0 ⇒ (UIncreasing(COND_LOAD2741(&&(>(i15[4], 0), >=(i21[4], i15[4])), i15[4], i21[4])), ≥)∧[(-1)bni_24 + (-1)Bound*bni_24] + [bni_24]i15[4] ≥ 0∧[(-1)bso_25] ≥ 0)



    We simplified constraint (26) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (27)    (i15[4] + [-1] ≥ 0∧i21[4] + [-1]i15[4] ≥ 0 ⇒ (UIncreasing(COND_LOAD2741(&&(>(i15[4], 0), >=(i21[4], i15[4])), i15[4], i21[4])), ≥)∧[(-1)bni_24 + (-1)Bound*bni_24] + [bni_24]i15[4] ≥ 0∧[(-1)bso_25] ≥ 0)



    We simplified constraint (27) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (28)    (i15[4] ≥ 0∧i21[4] + [-1] + [-1]i15[4] ≥ 0 ⇒ (UIncreasing(COND_LOAD2741(&&(>(i15[4], 0), >=(i21[4], i15[4])), i15[4], i21[4])), ≥)∧[(-1)Bound*bni_24] + [bni_24]i15[4] ≥ 0∧[(-1)bso_25] ≥ 0)



    We simplified constraint (28) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (29)    (i15[4] ≥ 0∧i21[4] ≥ 0 ⇒ (UIncreasing(COND_LOAD2741(&&(>(i15[4], 0), >=(i21[4], i15[4])), i15[4], i21[4])), ≥)∧[(-1)Bound*bni_24] + [bni_24]i15[4] ≥ 0∧[(-1)bso_25] ≥ 0)







For Pair COND_LOAD2741(TRUE, i15, i21) → LOAD139(+(i15, -1)) the following chains were created:
  • We consider the chain COND_LOAD2741(TRUE, i15[5], i21[5]) → LOAD139(+(i15[5], -1)) which results in the following constraint:

    (30)    (COND_LOAD2741(TRUE, i15[5], i21[5])≥NonInfC∧COND_LOAD2741(TRUE, i15[5], i21[5])≥LOAD139(+(i15[5], -1))∧(UIncreasing(LOAD139(+(i15[5], -1))), ≥))



    We simplified constraint (30) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (31)    ((UIncreasing(LOAD139(+(i15[5], -1))), ≥)∧[1 + (-1)bso_27] ≥ 0)



    We simplified constraint (31) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (32)    ((UIncreasing(LOAD139(+(i15[5], -1))), ≥)∧[1 + (-1)bso_27] ≥ 0)



    We simplified constraint (32) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (33)    ((UIncreasing(LOAD139(+(i15[5], -1))), ≥)∧[1 + (-1)bso_27] ≥ 0)



    We simplified constraint (33) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

    (34)    ((UIncreasing(LOAD139(+(i15[5], -1))), ≥)∧0 = 0∧0 = 0∧[1 + (-1)bso_27] ≥ 0)







To summarize, we get the following constraints P≥ for the following pairs.
  • LOAD139(i15) → COND_LOAD139(>(i15, 0), i15)
    • (i15[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD139(>(i15[0], 0), i15[0])), ≥)∧[(-1)Bound*bni_16] + [bni_16]i15[0] ≥ 0∧[(-1)bso_17] ≥ 0)

  • COND_LOAD139(TRUE, i15) → LOAD274(i15, 0)
    • ((UIncreasing(LOAD274(i15[1], 0)), ≥)∧0 = 0∧[(-1)bso_19] ≥ 0)

  • LOAD274(i15, i21) → COND_LOAD274(&&(&&(>=(i21, 0), <(i21, i15)), >(+(i21, 1), 0)), i15, i21)
    • (i21[2] ≥ 0∧i21[2] ≥ 0∧i15[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD274(&&(&&(>=(i21[2], 0), <(i21[2], i15[2])), >(+(i21[2], 1), 0)), i15[2], i21[2])), ≥)∧[(-1)Bound*bni_20] + [bni_20]i21[2] + [bni_20]i15[2] ≥ 0∧[(-1)bso_21] ≥ 0)

  • COND_LOAD274(TRUE, i15, i21) → LOAD274(i15, +(i21, 1))
    • ((UIncreasing(LOAD274(i15[3], +(i21[3], 1))), ≥)∧0 = 0∧0 = 0∧[(-1)bso_23] ≥ 0)

  • LOAD274(i15, i21) → COND_LOAD2741(&&(>(i15, 0), >=(i21, i15)), i15, i21)
    • (i15[4] ≥ 0∧i21[4] ≥ 0 ⇒ (UIncreasing(COND_LOAD2741(&&(>(i15[4], 0), >=(i21[4], i15[4])), i15[4], i21[4])), ≥)∧[(-1)Bound*bni_24] + [bni_24]i15[4] ≥ 0∧[(-1)bso_25] ≥ 0)

  • COND_LOAD2741(TRUE, i15, i21) → LOAD139(+(i15, -1))
    • ((UIncreasing(LOAD139(+(i15[5], -1))), ≥)∧0 = 0∧0 = 0∧[1 + (-1)bso_27] ≥ 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(LOAD139(x1)) = [-1] + x1   
POL(COND_LOAD139(x1, x2)) = [-1] + x2   
POL(>(x1, x2)) = [-1]   
POL(0) = 0   
POL(LOAD274(x1, x2)) = [-1] + x1   
POL(COND_LOAD274(x1, x2, x3)) = [-1] + x2   
POL(&&(x1, x2)) = [-1]   
POL(>=(x1, x2)) = [-1]   
POL(<(x1, x2)) = [-1]   
POL(+(x1, x2)) = x1 + x2   
POL(1) = [1]   
POL(COND_LOAD2741(x1, x2, x3)) = [-1] + x2   
POL(-1) = [-1]   

The following pairs are in P>:

COND_LOAD2741(TRUE, i15[5], i21[5]) → LOAD139(+(i15[5], -1))

The following pairs are in Pbound:

LOAD139(i15[0]) → COND_LOAD139(>(i15[0], 0), i15[0])
LOAD274(i15[2], i21[2]) → COND_LOAD274(&&(&&(>=(i21[2], 0), <(i21[2], i15[2])), >(+(i21[2], 1), 0)), i15[2], i21[2])
LOAD274(i15[4], i21[4]) → COND_LOAD2741(&&(>(i15[4], 0), >=(i21[4], i15[4])), i15[4], i21[4])

The following pairs are in P≥:

LOAD139(i15[0]) → COND_LOAD139(>(i15[0], 0), i15[0])
COND_LOAD139(TRUE, i15[1]) → LOAD274(i15[1], 0)
LOAD274(i15[2], i21[2]) → COND_LOAD274(&&(&&(>=(i21[2], 0), <(i21[2], i15[2])), >(+(i21[2], 1), 0)), i15[2], i21[2])
COND_LOAD274(TRUE, i15[3], i21[3]) → LOAD274(i15[3], +(i21[3], 1))
LOAD274(i15[4], i21[4]) → COND_LOAD2741(&&(>(i15[4], 0), >=(i21[4], i15[4])), i15[4], i21[4])

There are no usable rules.

(10) Complex Obligation (AND)

(11) 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, Boolean


R is empty.

The integer pair graph contains the following rules and edges:
(0): LOAD139(i15[0]) → COND_LOAD139(i15[0] > 0, i15[0])
(1): COND_LOAD139(TRUE, i15[1]) → LOAD274(i15[1], 0)
(2): LOAD274(i15[2], i21[2]) → COND_LOAD274(i21[2] >= 0 && i21[2] < i15[2] && i21[2] + 1 > 0, i15[2], i21[2])
(3): COND_LOAD274(TRUE, i15[3], i21[3]) → LOAD274(i15[3], i21[3] + 1)
(4): LOAD274(i15[4], i21[4]) → COND_LOAD2741(i15[4] > 0 && i21[4] >= i15[4], i15[4], i21[4])

(0) -> (1), if ((i15[0] →* i15[1])∧(i15[0] > 0 →* TRUE))


(1) -> (2), if ((0 →* i21[2])∧(i15[1] →* i15[2]))


(3) -> (2), if ((i21[3] + 1 →* i21[2])∧(i15[3] →* i15[2]))


(2) -> (3), if ((i15[2] →* i15[3])∧(i21[2] →* i21[3])∧(i21[2] >= 0 && i21[2] < i15[2] && i21[2] + 1 > 0 →* TRUE))


(1) -> (4), if ((0 →* i21[4])∧(i15[1] →* i15[4]))


(3) -> (4), if ((i21[3] + 1 →* i21[4])∧(i15[3] →* i15[4]))



The set Q consists of the following terms:
Load139(x0)
Cond_Load139(TRUE, x0)
Load274(x0, x1)
Cond_Load274(TRUE, x0, x1)
Cond_Load2741(TRUE, x0, x1)

(12) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 3 less nodes.

(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:

Integer, Boolean


R is empty.

The integer pair graph contains the following rules and edges:
(3): COND_LOAD274(TRUE, i15[3], i21[3]) → LOAD274(i15[3], i21[3] + 1)
(2): LOAD274(i15[2], i21[2]) → COND_LOAD274(i21[2] >= 0 && i21[2] < i15[2] && i21[2] + 1 > 0, i15[2], i21[2])

(3) -> (2), if ((i21[3] + 1 →* i21[2])∧(i15[3] →* i15[2]))


(2) -> (3), if ((i15[2] →* i15[3])∧(i21[2] →* i21[3])∧(i21[2] >= 0 && i21[2] < i15[2] && i21[2] + 1 > 0 →* TRUE))



The set Q consists of the following terms:
Load139(x0)
Cond_Load139(TRUE, x0)
Load274(x0, x1)
Cond_Load274(TRUE, x0, x1)
Cond_Load2741(TRUE, x0, x1)

(14) 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 COND_LOAD274(TRUE, i15[3], i21[3]) → LOAD274(i15[3], +(i21[3], 1)) the following chains were created:
  • We consider the chain COND_LOAD274(TRUE, i15[3], i21[3]) → LOAD274(i15[3], +(i21[3], 1)) which results in the following constraint:

    (1)    (COND_LOAD274(TRUE, i15[3], i21[3])≥NonInfC∧COND_LOAD274(TRUE, i15[3], i21[3])≥LOAD274(i15[3], +(i21[3], 1))∧(UIncreasing(LOAD274(i15[3], +(i21[3], 1))), ≥))



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

    (2)    ((UIncreasing(LOAD274(i15[3], +(i21[3], 1))), ≥)∧[1 + (-1)bso_11] ≥ 0)



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

    (3)    ((UIncreasing(LOAD274(i15[3], +(i21[3], 1))), ≥)∧[1 + (-1)bso_11] ≥ 0)



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

    (4)    ((UIncreasing(LOAD274(i15[3], +(i21[3], 1))), ≥)∧[1 + (-1)bso_11] ≥ 0)



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

    (5)    ((UIncreasing(LOAD274(i15[3], +(i21[3], 1))), ≥)∧0 = 0∧0 = 0∧[1 + (-1)bso_11] ≥ 0)







For Pair LOAD274(i15[2], i21[2]) → COND_LOAD274(&&(&&(>=(i21[2], 0), <(i21[2], i15[2])), >(+(i21[2], 1), 0)), i15[2], i21[2]) the following chains were created:
  • We consider the chain LOAD274(i15[2], i21[2]) → COND_LOAD274(&&(&&(>=(i21[2], 0), <(i21[2], i15[2])), >(+(i21[2], 1), 0)), i15[2], i21[2]), COND_LOAD274(TRUE, i15[3], i21[3]) → LOAD274(i15[3], +(i21[3], 1)) which results in the following constraint:

    (6)    (i15[2]=i15[3]∧i21[2]=i21[3]∧&&(&&(>=(i21[2], 0), <(i21[2], i15[2])), >(+(i21[2], 1), 0))=TRUE ⇒ LOAD274(i15[2], i21[2])≥NonInfC∧LOAD274(i15[2], i21[2])≥COND_LOAD274(&&(&&(>=(i21[2], 0), <(i21[2], i15[2])), >(+(i21[2], 1), 0)), i15[2], i21[2])∧(UIncreasing(COND_LOAD274(&&(&&(>=(i21[2], 0), <(i21[2], i15[2])), >(+(i21[2], 1), 0)), i15[2], i21[2])), ≥))



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

    (7)    (>(+(i21[2], 1), 0)=TRUE∧>=(i21[2], 0)=TRUE∧<(i21[2], i15[2])=TRUE ⇒ LOAD274(i15[2], i21[2])≥NonInfC∧LOAD274(i15[2], i21[2])≥COND_LOAD274(&&(&&(>=(i21[2], 0), <(i21[2], i15[2])), >(+(i21[2], 1), 0)), i15[2], i21[2])∧(UIncreasing(COND_LOAD274(&&(&&(>=(i21[2], 0), <(i21[2], i15[2])), >(+(i21[2], 1), 0)), i15[2], i21[2])), ≥))



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

    (8)    (i21[2] ≥ 0∧i21[2] ≥ 0∧i15[2] + [-1] + [-1]i21[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD274(&&(&&(>=(i21[2], 0), <(i21[2], i15[2])), >(+(i21[2], 1), 0)), i15[2], i21[2])), ≥)∧[(-1)bni_12 + (-1)Bound*bni_12] + [(-1)bni_12]i21[2] + [bni_12]i15[2] ≥ 0∧[(-1)bso_13] ≥ 0)



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

    (9)    (i21[2] ≥ 0∧i21[2] ≥ 0∧i15[2] + [-1] + [-1]i21[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD274(&&(&&(>=(i21[2], 0), <(i21[2], i15[2])), >(+(i21[2], 1), 0)), i15[2], i21[2])), ≥)∧[(-1)bni_12 + (-1)Bound*bni_12] + [(-1)bni_12]i21[2] + [bni_12]i15[2] ≥ 0∧[(-1)bso_13] ≥ 0)



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

    (10)    (i21[2] ≥ 0∧i21[2] ≥ 0∧i15[2] + [-1] + [-1]i21[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD274(&&(&&(>=(i21[2], 0), <(i21[2], i15[2])), >(+(i21[2], 1), 0)), i15[2], i21[2])), ≥)∧[(-1)bni_12 + (-1)Bound*bni_12] + [(-1)bni_12]i21[2] + [bni_12]i15[2] ≥ 0∧[(-1)bso_13] ≥ 0)



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

    (11)    (i21[2] ≥ 0∧i21[2] ≥ 0∧i15[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD274(&&(&&(>=(i21[2], 0), <(i21[2], i15[2])), >(+(i21[2], 1), 0)), i15[2], i21[2])), ≥)∧[(-1)Bound*bni_12] + [bni_12]i15[2] ≥ 0∧[(-1)bso_13] ≥ 0)







To summarize, we get the following constraints P≥ for the following pairs.
  • COND_LOAD274(TRUE, i15[3], i21[3]) → LOAD274(i15[3], +(i21[3], 1))
    • ((UIncreasing(LOAD274(i15[3], +(i21[3], 1))), ≥)∧0 = 0∧0 = 0∧[1 + (-1)bso_11] ≥ 0)

  • LOAD274(i15[2], i21[2]) → COND_LOAD274(&&(&&(>=(i21[2], 0), <(i21[2], i15[2])), >(+(i21[2], 1), 0)), i15[2], i21[2])
    • (i21[2] ≥ 0∧i21[2] ≥ 0∧i15[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD274(&&(&&(>=(i21[2], 0), <(i21[2], i15[2])), >(+(i21[2], 1), 0)), i15[2], i21[2])), ≥)∧[(-1)Bound*bni_12] + [bni_12]i15[2] ≥ 0∧[(-1)bso_13] ≥ 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(COND_LOAD274(x1, x2, x3)) = [-1] + x2 + [-1]x3   
POL(LOAD274(x1, x2)) = [-1] + [-1]x2 + x1   
POL(+(x1, x2)) = x1 + x2   
POL(1) = [1]   
POL(&&(x1, x2)) = [-1]   
POL(>=(x1, x2)) = [-1]   
POL(0) = 0   
POL(<(x1, x2)) = [-1]   
POL(>(x1, x2)) = [-1]   

The following pairs are in P>:

COND_LOAD274(TRUE, i15[3], i21[3]) → LOAD274(i15[3], +(i21[3], 1))

The following pairs are in Pbound:

LOAD274(i15[2], i21[2]) → COND_LOAD274(&&(&&(>=(i21[2], 0), <(i21[2], i15[2])), >(+(i21[2], 1), 0)), i15[2], i21[2])

The following pairs are in P≥:

LOAD274(i15[2], i21[2]) → COND_LOAD274(&&(&&(>=(i21[2], 0), <(i21[2], i15[2])), >(+(i21[2], 1), 0)), i15[2], i21[2])

There are no usable rules.

(15) Complex Obligation (AND)

(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:

Boolean, Integer


R is empty.

The integer pair graph contains the following rules and edges:
(2): LOAD274(i15[2], i21[2]) → COND_LOAD274(i21[2] >= 0 && i21[2] < i15[2] && i21[2] + 1 > 0, i15[2], i21[2])


The set Q consists of the following terms:
Load139(x0)
Cond_Load139(TRUE, x0)
Load274(x0, x1)
Cond_Load274(TRUE, x0, x1)
Cond_Load2741(TRUE, x0, x1)

(17) IDependencyGraphProof (EQUIVALENT transformation)

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

(18) TRUE

(19) 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:
(3): COND_LOAD274(TRUE, i15[3], i21[3]) → LOAD274(i15[3], i21[3] + 1)


The set Q consists of the following terms:
Load139(x0)
Cond_Load139(TRUE, x0)
Load274(x0, x1)
Cond_Load274(TRUE, x0, x1)
Cond_Load2741(TRUE, x0, x1)

(20) IDependencyGraphProof (EQUIVALENT transformation)

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

(21) TRUE

(22) 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_LOAD139(TRUE, i15[1]) → LOAD274(i15[1], 0)
(3): COND_LOAD274(TRUE, i15[3], i21[3]) → LOAD274(i15[3], i21[3] + 1)
(5): COND_LOAD2741(TRUE, i15[5], i21[5]) → LOAD139(i15[5] + -1)


The set Q consists of the following terms:
Load139(x0)
Cond_Load139(TRUE, x0)
Load274(x0, x1)
Cond_Load274(TRUE, x0, x1)
Cond_Load2741(TRUE, x0, x1)

(23) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 3 less nodes.

(24) TRUE