Termination of the given JBC could be proven:

0 JBC
↳1 JBC2FIG (⇐)
↳2 FIGraph
↳3 FIGtoITRSProof (⇐)
↳4 ITRS
↳5 GroundTermsRemoverProof (⇔)
↳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: LogAG

(1) JBC2FIG (SOUND transformation)

Constructed FIGraph.

(2) Obligation:

FIGraph based on JBC Program:
Graph of 138 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:
Load416(1, i36, i33) → Cond_Load416(i36 > 1, 1, i36, i33)
Cond_Load416(TRUE, 1, i36, i33) → Load583(1, i36, i33, i36 - 2, 0)
Load583(1, i36, i33, i51, i48) → Cond_Load583(i51 > 1 && i48 + 1 > 0, 1, i36, i33, i51, i48)
Cond_Load583(TRUE, 1, i36, i33, i51, i48) → Load583(1, i36, i33, i51 - 2, i48 + 1)
Load583(1, i36, i33, i51, i48) → Cond_Load5831(i51 > 0 && i51 <= 1, 1, i36, i33, i51, i48)
Cond_Load5831(TRUE, 1, i36, i33, i51, i48) → Load594(1, i36, i33, i48)
Load594(1, i36, i33, i48) → Load416(1, i48 + 1, i33 + 1)
Load583(1, i36, i33, i50, i48) → Cond_Load5832(i50 <= 1 && i33 + 1 > 0 && i48 + 1 > 0, 1, i36, i33, i50, i48)
Cond_Load5832(TRUE, 1, i36, i33, i50, i48) → Load416(1, i48 + 1, i33 + 1)
The set Q consists of the following terms:
Load416(1, x0, x1)
Cond_Load416(TRUE, 1, x0, x1)
Load583(1, x0, x1, x2, x3)
Cond_Load583(TRUE, 1, x0, x1, x2, x3)
Cond_Load5831(TRUE, 1, x0, x1, x2, x3)
Load594(1, x0, x1, x2)
Cond_Load5832(TRUE, 1, x0, x1, x2, x3)

(5) GroundTermsRemoverProof (EQUIVALENT transformation)

Some arguments are removed because they always contain the same ground term.
We removed the following ground terms:
  • 1

We removed arguments according to the following replacements:

Cond_Load5832(x1, x2, x3, x4, x5, x6) → Cond_Load5832(x1, x3, x4, x5, x6)
Load583(x1, x2, x3, x4, x5) → Load583(x2, x3, x4, x5)
Load416(x1, x2, x3) → Load416(x2, x3)
Load594(x1, x2, x3, x4) → Load594(x2, x3, x4)
Cond_Load5831(x1, x2, x3, x4, x5, x6) → Cond_Load5831(x1, x3, x4, x5, x6)
Cond_Load583(x1, x2, x3, x4, x5, x6) → Cond_Load583(x1, x3, x4, x5, x6)
Cond_Load416(x1, x2, x3, x4) → Cond_Load416(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:
Load416(i36, i33) → Cond_Load416(i36 > 1, i36, i33)
Cond_Load416(TRUE, i36, i33) → Load583(i36, i33, i36 - 2, 0)
Load583(i36, i33, i51, i48) → Cond_Load583(i51 > 1 && i48 + 1 > 0, i36, i33, i51, i48)
Cond_Load583(TRUE, i36, i33, i51, i48) → Load583(i36, i33, i51 - 2, i48 + 1)
Load583(i36, i33, i51, i48) → Cond_Load5831(i51 > 0 && i51 <= 1, i36, i33, i51, i48)
Cond_Load5831(TRUE, i36, i33, i51, i48) → Load594(i36, i33, i48)
Load594(i36, i33, i48) → Load416(i48 + 1, i33 + 1)
Load583(i36, i33, i50, i48) → Cond_Load5832(i50 <= 1 && i33 + 1 > 0 && i48 + 1 > 0, i36, i33, i50, i48)
Cond_Load5832(TRUE, i36, i33, i50, i48) → Load416(i48 + 1, i33 + 1)
The set Q consists of the following terms:
Load416(x0, x1)
Cond_Load416(TRUE, x0, x1)
Load583(x0, x1, x2, x3)
Cond_Load583(TRUE, x0, x1, x2, x3)
Cond_Load5831(TRUE, x0, x1, x2, x3)
Load594(x0, x1, x2)
Cond_Load5832(TRUE, x0, x1, x2, x3)

(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:

Integer, Boolean


The ITRS R consists of the following rules:
Load416(i36, i33) → Cond_Load416(i36 > 1, i36, i33)
Cond_Load416(TRUE, i36, i33) → Load583(i36, i33, i36 - 2, 0)
Load583(i36, i33, i51, i48) → Cond_Load583(i51 > 1 && i48 + 1 > 0, i36, i33, i51, i48)
Cond_Load583(TRUE, i36, i33, i51, i48) → Load583(i36, i33, i51 - 2, i48 + 1)
Load583(i36, i33, i51, i48) → Cond_Load5831(i51 > 0 && i51 <= 1, i36, i33, i51, i48)
Cond_Load5831(TRUE, i36, i33, i51, i48) → Load594(i36, i33, i48)
Load594(i36, i33, i48) → Load416(i48 + 1, i33 + 1)
Load583(i36, i33, i50, i48) → Cond_Load5832(i50 <= 1 && i33 + 1 > 0 && i48 + 1 > 0, i36, i33, i50, i48)
Cond_Load5832(TRUE, i36, i33, i50, i48) → Load416(i48 + 1, i33 + 1)

The integer pair graph contains the following rules and edges:
(0): LOAD416(i36[0], i33[0]) → COND_LOAD416(i36[0] > 1, i36[0], i33[0])
(1): COND_LOAD416(TRUE, i36[1], i33[1]) → LOAD583(i36[1], i33[1], i36[1] - 2, 0)
(2): LOAD583(i36[2], i33[2], i51[2], i48[2]) → COND_LOAD583(i51[2] > 1 && i48[2] + 1 > 0, i36[2], i33[2], i51[2], i48[2])
(3): COND_LOAD583(TRUE, i36[3], i33[3], i51[3], i48[3]) → LOAD583(i36[3], i33[3], i51[3] - 2, i48[3] + 1)
(4): LOAD583(i36[4], i33[4], i51[4], i48[4]) → COND_LOAD5831(i51[4] > 0 && i51[4] <= 1, i36[4], i33[4], i51[4], i48[4])
(5): COND_LOAD5831(TRUE, i36[5], i33[5], i51[5], i48[5]) → LOAD594(i36[5], i33[5], i48[5])
(6): LOAD594(i36[6], i33[6], i48[6]) → LOAD416(i48[6] + 1, i33[6] + 1)
(7): LOAD583(i36[7], i33[7], i50[7], i48[7]) → COND_LOAD5832(i50[7] <= 1 && i33[7] + 1 > 0 && i48[7] + 1 > 0, i36[7], i33[7], i50[7], i48[7])
(8): COND_LOAD5832(TRUE, i36[8], i33[8], i50[8], i48[8]) → LOAD416(i48[8] + 1, i33[8] + 1)

(0) -> (1), if ((i33[0] →* i33[1])∧(i36[0] > 1 →* TRUE)∧(i36[0] →* i36[1]))


(1) -> (2), if ((0 →* i48[2])∧(i36[1] - 2 →* i51[2])∧(i33[1] →* i33[2])∧(i36[1] →* i36[2]))


(1) -> (4), if ((i33[1] →* i33[4])∧(i36[1] →* i36[4])∧(0 →* i48[4])∧(i36[1] - 2 →* i51[4]))


(1) -> (7), if ((i36[1] - 2 →* i50[7])∧(i33[1] →* i33[7])∧(0 →* i48[7])∧(i36[1] →* i36[7]))


(2) -> (3), if ((i36[2] →* i36[3])∧(i51[2] →* i51[3])∧(i33[2] →* i33[3])∧(i48[2] →* i48[3])∧(i51[2] > 1 && i48[2] + 1 > 0 →* TRUE))


(3) -> (2), if ((i48[3] + 1 →* i48[2])∧(i51[3] - 2 →* i51[2])∧(i33[3] →* i33[2])∧(i36[3] →* i36[2]))


(3) -> (4), if ((i48[3] + 1 →* i48[4])∧(i36[3] →* i36[4])∧(i33[3] →* i33[4])∧(i51[3] - 2 →* i51[4]))


(3) -> (7), if ((i48[3] + 1 →* i48[7])∧(i51[3] - 2 →* i50[7])∧(i36[3] →* i36[7])∧(i33[3] →* i33[7]))


(4) -> (5), if ((i51[4] > 0 && i51[4] <= 1 →* TRUE)∧(i36[4] →* i36[5])∧(i51[4] →* i51[5])∧(i48[4] →* i48[5])∧(i33[4] →* i33[5]))


(5) -> (6), if ((i48[5] →* i48[6])∧(i36[5] →* i36[6])∧(i33[5] →* i33[6]))


(6) -> (0), if ((i33[6] + 1 →* i33[0])∧(i48[6] + 1 →* i36[0]))


(7) -> (8), if ((i50[7] →* i50[8])∧(i33[7] →* i33[8])∧(i36[7] →* i36[8])∧(i48[7] →* i48[8])∧(i50[7] <= 1 && i33[7] + 1 > 0 && i48[7] + 1 > 0 →* TRUE))


(8) -> (0), if ((i48[8] + 1 →* i36[0])∧(i33[8] + 1 →* i33[0]))



The set Q consists of the following terms:
Load416(x0, x1)
Cond_Load416(TRUE, x0, x1)
Load583(x0, x1, x2, x3)
Cond_Load583(TRUE, x0, x1, x2, x3)
Cond_Load5831(TRUE, x0, x1, x2, x3)
Load594(x0, x1, x2)
Cond_Load5832(TRUE, x0, x1, x2, x3)

(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:

Integer, Boolean


R is empty.

The integer pair graph contains the following rules and edges:
(0): LOAD416(i36[0], i33[0]) → COND_LOAD416(i36[0] > 1, i36[0], i33[0])
(1): COND_LOAD416(TRUE, i36[1], i33[1]) → LOAD583(i36[1], i33[1], i36[1] - 2, 0)
(2): LOAD583(i36[2], i33[2], i51[2], i48[2]) → COND_LOAD583(i51[2] > 1 && i48[2] + 1 > 0, i36[2], i33[2], i51[2], i48[2])
(3): COND_LOAD583(TRUE, i36[3], i33[3], i51[3], i48[3]) → LOAD583(i36[3], i33[3], i51[3] - 2, i48[3] + 1)
(4): LOAD583(i36[4], i33[4], i51[4], i48[4]) → COND_LOAD5831(i51[4] > 0 && i51[4] <= 1, i36[4], i33[4], i51[4], i48[4])
(5): COND_LOAD5831(TRUE, i36[5], i33[5], i51[5], i48[5]) → LOAD594(i36[5], i33[5], i48[5])
(6): LOAD594(i36[6], i33[6], i48[6]) → LOAD416(i48[6] + 1, i33[6] + 1)
(7): LOAD583(i36[7], i33[7], i50[7], i48[7]) → COND_LOAD5832(i50[7] <= 1 && i33[7] + 1 > 0 && i48[7] + 1 > 0, i36[7], i33[7], i50[7], i48[7])
(8): COND_LOAD5832(TRUE, i36[8], i33[8], i50[8], i48[8]) → LOAD416(i48[8] + 1, i33[8] + 1)

(0) -> (1), if ((i33[0] →* i33[1])∧(i36[0] > 1 →* TRUE)∧(i36[0] →* i36[1]))


(1) -> (2), if ((0 →* i48[2])∧(i36[1] - 2 →* i51[2])∧(i33[1] →* i33[2])∧(i36[1] →* i36[2]))


(1) -> (4), if ((i33[1] →* i33[4])∧(i36[1] →* i36[4])∧(0 →* i48[4])∧(i36[1] - 2 →* i51[4]))


(1) -> (7), if ((i36[1] - 2 →* i50[7])∧(i33[1] →* i33[7])∧(0 →* i48[7])∧(i36[1] →* i36[7]))


(2) -> (3), if ((i36[2] →* i36[3])∧(i51[2] →* i51[3])∧(i33[2] →* i33[3])∧(i48[2] →* i48[3])∧(i51[2] > 1 && i48[2] + 1 > 0 →* TRUE))


(3) -> (2), if ((i48[3] + 1 →* i48[2])∧(i51[3] - 2 →* i51[2])∧(i33[3] →* i33[2])∧(i36[3] →* i36[2]))


(3) -> (4), if ((i48[3] + 1 →* i48[4])∧(i36[3] →* i36[4])∧(i33[3] →* i33[4])∧(i51[3] - 2 →* i51[4]))


(3) -> (7), if ((i48[3] + 1 →* i48[7])∧(i51[3] - 2 →* i50[7])∧(i36[3] →* i36[7])∧(i33[3] →* i33[7]))


(4) -> (5), if ((i51[4] > 0 && i51[4] <= 1 →* TRUE)∧(i36[4] →* i36[5])∧(i51[4] →* i51[5])∧(i48[4] →* i48[5])∧(i33[4] →* i33[5]))


(5) -> (6), if ((i48[5] →* i48[6])∧(i36[5] →* i36[6])∧(i33[5] →* i33[6]))


(6) -> (0), if ((i33[6] + 1 →* i33[0])∧(i48[6] + 1 →* i36[0]))


(7) -> (8), if ((i50[7] →* i50[8])∧(i33[7] →* i33[8])∧(i36[7] →* i36[8])∧(i48[7] →* i48[8])∧(i50[7] <= 1 && i33[7] + 1 > 0 && i48[7] + 1 > 0 →* TRUE))


(8) -> (0), if ((i48[8] + 1 →* i36[0])∧(i33[8] + 1 →* i33[0]))



The set Q consists of the following terms:
Load416(x0, x1)
Cond_Load416(TRUE, x0, x1)
Load583(x0, x1, x2, x3)
Cond_Load583(TRUE, x0, x1, x2, x3)
Cond_Load5831(TRUE, x0, x1, x2, x3)
Load594(x0, x1, x2)
Cond_Load5832(TRUE, x0, x1, x2, x3)

(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 LOAD416(i36, i33) → COND_LOAD416(>(i36, 1), i36, i33) the following chains were created:
  • We consider the chain LOAD416(i36[0], i33[0]) → COND_LOAD416(>(i36[0], 1), i36[0], i33[0]), COND_LOAD416(TRUE, i36[1], i33[1]) → LOAD583(i36[1], i33[1], -(i36[1], 2), 0) which results in the following constraint:

    (1)    (i33[0]=i33[1]∧>(i36[0], 1)=TRUE∧i36[0]=i36[1] ⇒ LOAD416(i36[0], i33[0])≥NonInfC∧LOAD416(i36[0], i33[0])≥COND_LOAD416(>(i36[0], 1), i36[0], i33[0])∧(UIncreasing(COND_LOAD416(>(i36[0], 1), i36[0], i33[0])), ≥))



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

    (2)    (>(i36[0], 1)=TRUE ⇒ LOAD416(i36[0], i33[0])≥NonInfC∧LOAD416(i36[0], i33[0])≥COND_LOAD416(>(i36[0], 1), i36[0], i33[0])∧(UIncreasing(COND_LOAD416(>(i36[0], 1), i36[0], i33[0])), ≥))



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

    (3)    (i36[0] + [-2] ≥ 0 ⇒ (UIncreasing(COND_LOAD416(>(i36[0], 1), i36[0], i33[0])), ≥)∧[(-1)bni_40 + (-1)Bound*bni_40] + [bni_40]i36[0] ≥ 0∧[(-1)bso_41] ≥ 0)



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

    (4)    (i36[0] + [-2] ≥ 0 ⇒ (UIncreasing(COND_LOAD416(>(i36[0], 1), i36[0], i33[0])), ≥)∧[(-1)bni_40 + (-1)Bound*bni_40] + [bni_40]i36[0] ≥ 0∧[(-1)bso_41] ≥ 0)



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

    (5)    (i36[0] + [-2] ≥ 0 ⇒ (UIncreasing(COND_LOAD416(>(i36[0], 1), i36[0], i33[0])), ≥)∧[(-1)bni_40 + (-1)Bound*bni_40] + [bni_40]i36[0] ≥ 0∧[(-1)bso_41] ≥ 0)



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

    (6)    (i36[0] + [-2] ≥ 0 ⇒ (UIncreasing(COND_LOAD416(>(i36[0], 1), i36[0], i33[0])), ≥)∧0 = 0∧[(-1)bni_40 + (-1)Bound*bni_40] + [bni_40]i36[0] ≥ 0∧0 = 0∧[(-1)bso_41] ≥ 0)



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

    (7)    (i36[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD416(>(i36[0], 1), i36[0], i33[0])), ≥)∧0 = 0∧[bni_40 + (-1)Bound*bni_40] + [bni_40]i36[0] ≥ 0∧0 = 0∧[(-1)bso_41] ≥ 0)







For Pair COND_LOAD416(TRUE, i36, i33) → LOAD583(i36, i33, -(i36, 2), 0) the following chains were created:
  • We consider the chain COND_LOAD5831(TRUE, i36[5], i33[5], i51[5], i48[5]) → LOAD594(i36[5], i33[5], i48[5]), LOAD594(i36[6], i33[6], i48[6]) → LOAD416(+(i48[6], 1), +(i33[6], 1)), LOAD416(i36[0], i33[0]) → COND_LOAD416(>(i36[0], 1), i36[0], i33[0]), COND_LOAD416(TRUE, i36[1], i33[1]) → LOAD583(i36[1], i33[1], -(i36[1], 2), 0), LOAD583(i36[2], i33[2], i51[2], i48[2]) → COND_LOAD583(&&(>(i51[2], 1), >(+(i48[2], 1), 0)), i36[2], i33[2], i51[2], i48[2]), COND_LOAD583(TRUE, i36[3], i33[3], i51[3], i48[3]) → LOAD583(i36[3], i33[3], -(i51[3], 2), +(i48[3], 1)) which results in the following constraint:

    (8)    (i48[5]=i48[6]∧i36[5]=i36[6]∧i33[5]=i33[6]∧+(i33[6], 1)=i33[0]∧+(i48[6], 1)=i36[0]∧i33[0]=i33[1]∧>(i36[0], 1)=TRUE∧i36[0]=i36[1]∧0=i48[2]∧-(i36[1], 2)=i51[2]∧i33[1]=i33[2]∧i36[1]=i36[2]∧i36[2]=i36[3]∧i51[2]=i51[3]∧i33[2]=i33[3]∧i48[2]=i48[3]∧&&(>(i51[2], 1), >(+(i48[2], 1), 0))=TRUE ⇒ COND_LOAD416(TRUE, i36[1], i33[1])≥NonInfC∧COND_LOAD416(TRUE, i36[1], i33[1])≥LOAD583(i36[1], i33[1], -(i36[1], 2), 0)∧(UIncreasing(LOAD583(i36[1], i33[1], -(i36[1], 2), 0)), ≥))



    We simplified constraint (8) using rules (III), (IV), (IDP_CONSTANT_FOLD), (DELETE_TRIVIAL_REDUCESTO), (IDP_BOOLEAN) which results in the following new constraint:

    (9)    (>(+(i48[6], 1), 1)=TRUE∧>(-(+(i48[6], 1), 2), 1)=TRUE ⇒ COND_LOAD416(TRUE, +(i48[6], 1), +(i33[6], 1))≥NonInfC∧COND_LOAD416(TRUE, +(i48[6], 1), +(i33[6], 1))≥LOAD583(+(i48[6], 1), +(i33[6], 1), -(+(i48[6], 1), 2), 0)∧(UIncreasing(LOAD583(i36[1], i33[1], -(i36[1], 2), 0)), ≥))



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

    (10)    (i48[6] + [-1] ≥ 0∧i48[6] + [-3] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[1], i33[1], -(i36[1], 2), 0)), ≥)∧[(-1)Bound*bni_42] + [bni_42]i48[6] ≥ 0∧[1 + (-1)bso_43] ≥ 0)



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

    (11)    (i48[6] + [-1] ≥ 0∧i48[6] + [-3] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[1], i33[1], -(i36[1], 2), 0)), ≥)∧[(-1)Bound*bni_42] + [bni_42]i48[6] ≥ 0∧[1 + (-1)bso_43] ≥ 0)



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

    (12)    (i48[6] + [-1] ≥ 0∧i48[6] + [-3] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[1], i33[1], -(i36[1], 2), 0)), ≥)∧[(-1)Bound*bni_42] + [bni_42]i48[6] ≥ 0∧[1 + (-1)bso_43] ≥ 0)



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

    (13)    (i48[6] + [-1] ≥ 0∧i48[6] + [-3] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[1], i33[1], -(i36[1], 2), 0)), ≥)∧0 = 0∧[(-1)Bound*bni_42] + [bni_42]i48[6] ≥ 0∧0 = 0∧[1 + (-1)bso_43] ≥ 0)



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

    (14)    (i48[6] ≥ 0∧[-2] + i48[6] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[1], i33[1], -(i36[1], 2), 0)), ≥)∧0 = 0∧[(-1)Bound*bni_42 + bni_42] + [bni_42]i48[6] ≥ 0∧0 = 0∧[1 + (-1)bso_43] ≥ 0)



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

    (15)    ([2] + i48[6] ≥ 0∧i48[6] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[1], i33[1], -(i36[1], 2), 0)), ≥)∧0 = 0∧[(-1)Bound*bni_42 + (3)bni_42] + [bni_42]i48[6] ≥ 0∧0 = 0∧[1 + (-1)bso_43] ≥ 0)



  • We consider the chain COND_LOAD5831(TRUE, i36[5], i33[5], i51[5], i48[5]) → LOAD594(i36[5], i33[5], i48[5]), LOAD594(i36[6], i33[6], i48[6]) → LOAD416(+(i48[6], 1), +(i33[6], 1)), LOAD416(i36[0], i33[0]) → COND_LOAD416(>(i36[0], 1), i36[0], i33[0]), COND_LOAD416(TRUE, i36[1], i33[1]) → LOAD583(i36[1], i33[1], -(i36[1], 2), 0), LOAD583(i36[4], i33[4], i51[4], i48[4]) → COND_LOAD5831(&&(>(i51[4], 0), <=(i51[4], 1)), i36[4], i33[4], i51[4], i48[4]), COND_LOAD5831(TRUE, i36[5], i33[5], i51[5], i48[5]) → LOAD594(i36[5], i33[5], i48[5]) which results in the following constraint:

    (16)    (i48[5]=i48[6]∧i36[5]=i36[6]∧i33[5]=i33[6]∧+(i33[6], 1)=i33[0]∧+(i48[6], 1)=i36[0]∧i33[0]=i33[1]∧>(i36[0], 1)=TRUE∧i36[0]=i36[1]∧i33[1]=i33[4]∧i36[1]=i36[4]∧0=i48[4]∧-(i36[1], 2)=i51[4]∧&&(>(i51[4], 0), <=(i51[4], 1))=TRUE∧i36[4]=i36[5]1∧i51[4]=i51[5]1∧i48[4]=i48[5]1∧i33[4]=i33[5]1 ⇒ COND_LOAD416(TRUE, i36[1], i33[1])≥NonInfC∧COND_LOAD416(TRUE, i36[1], i33[1])≥LOAD583(i36[1], i33[1], -(i36[1], 2), 0)∧(UIncreasing(LOAD583(i36[1], i33[1], -(i36[1], 2), 0)), ≥))



    We simplified constraint (16) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (17)    (>(+(i48[6], 1), 1)=TRUE∧>(-(+(i48[6], 1), 2), 0)=TRUE∧<=(-(+(i48[6], 1), 2), 1)=TRUE ⇒ COND_LOAD416(TRUE, +(i48[6], 1), +(i33[6], 1))≥NonInfC∧COND_LOAD416(TRUE, +(i48[6], 1), +(i33[6], 1))≥LOAD583(+(i48[6], 1), +(i33[6], 1), -(+(i48[6], 1), 2), 0)∧(UIncreasing(LOAD583(i36[1], i33[1], -(i36[1], 2), 0)), ≥))



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

    (18)    (i48[6] + [-1] ≥ 0∧i48[6] + [-2] ≥ 0∧[2] + [-1]i48[6] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[1], i33[1], -(i36[1], 2), 0)), ≥)∧[(-1)Bound*bni_42] + [bni_42]i48[6] ≥ 0∧[1 + (-1)bso_43] ≥ 0)



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

    (19)    (i48[6] + [-1] ≥ 0∧i48[6] + [-2] ≥ 0∧[2] + [-1]i48[6] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[1], i33[1], -(i36[1], 2), 0)), ≥)∧[(-1)Bound*bni_42] + [bni_42]i48[6] ≥ 0∧[1 + (-1)bso_43] ≥ 0)



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

    (20)    (i48[6] + [-1] ≥ 0∧i48[6] + [-2] ≥ 0∧[2] + [-1]i48[6] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[1], i33[1], -(i36[1], 2), 0)), ≥)∧[(-1)Bound*bni_42] + [bni_42]i48[6] ≥ 0∧[1 + (-1)bso_43] ≥ 0)



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

    (21)    (i48[6] + [-1] ≥ 0∧i48[6] + [-2] ≥ 0∧[2] + [-1]i48[6] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[1], i33[1], -(i36[1], 2), 0)), ≥)∧0 = 0∧[(-1)Bound*bni_42] + [bni_42]i48[6] ≥ 0∧0 = 0∧[1 + (-1)bso_43] ≥ 0)



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

    (22)    (i48[6] ≥ 0∧[-1] + i48[6] ≥ 0∧[1] + [-1]i48[6] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[1], i33[1], -(i36[1], 2), 0)), ≥)∧0 = 0∧[(-1)Bound*bni_42 + bni_42] + [bni_42]i48[6] ≥ 0∧0 = 0∧[1 + (-1)bso_43] ≥ 0)



    We simplified constraint (22) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (23)    ([1] + i48[6] ≥ 0∧i48[6] ≥ 0∧[-1]i48[6] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[1], i33[1], -(i36[1], 2), 0)), ≥)∧0 = 0∧[(-1)Bound*bni_42 + (2)bni_42] + [bni_42]i48[6] ≥ 0∧0 = 0∧[1 + (-1)bso_43] ≥ 0)



    We simplified constraint (23) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (24)    ([1] ≥ 0∧0 ≥ 0∧0 ≥ 0 ⇒ (UIncreasing(LOAD583(i36[1], i33[1], -(i36[1], 2), 0)), ≥)∧0 = 0∧[(-1)Bound*bni_42 + (2)bni_42] ≥ 0∧0 = 0∧[1 + (-1)bso_43] ≥ 0)



  • We consider the chain COND_LOAD5831(TRUE, i36[5], i33[5], i51[5], i48[5]) → LOAD594(i36[5], i33[5], i48[5]), LOAD594(i36[6], i33[6], i48[6]) → LOAD416(+(i48[6], 1), +(i33[6], 1)), LOAD416(i36[0], i33[0]) → COND_LOAD416(>(i36[0], 1), i36[0], i33[0]), COND_LOAD416(TRUE, i36[1], i33[1]) → LOAD583(i36[1], i33[1], -(i36[1], 2), 0), LOAD583(i36[7], i33[7], i50[7], i48[7]) → COND_LOAD5832(&&(&&(<=(i50[7], 1), >(+(i33[7], 1), 0)), >(+(i48[7], 1), 0)), i36[7], i33[7], i50[7], i48[7]), COND_LOAD5832(TRUE, i36[8], i33[8], i50[8], i48[8]) → LOAD416(+(i48[8], 1), +(i33[8], 1)) which results in the following constraint:

    (25)    (i48[5]=i48[6]∧i36[5]=i36[6]∧i33[5]=i33[6]∧+(i33[6], 1)=i33[0]∧+(i48[6], 1)=i36[0]∧i33[0]=i33[1]∧>(i36[0], 1)=TRUE∧i36[0]=i36[1]∧-(i36[1], 2)=i50[7]∧i33[1]=i33[7]∧0=i48[7]∧i36[1]=i36[7]∧i50[7]=i50[8]∧i33[7]=i33[8]∧i36[7]=i36[8]∧i48[7]=i48[8]∧&&(&&(<=(i50[7], 1), >(+(i33[7], 1), 0)), >(+(i48[7], 1), 0))=TRUE ⇒ COND_LOAD416(TRUE, i36[1], i33[1])≥NonInfC∧COND_LOAD416(TRUE, i36[1], i33[1])≥LOAD583(i36[1], i33[1], -(i36[1], 2), 0)∧(UIncreasing(LOAD583(i36[1], i33[1], -(i36[1], 2), 0)), ≥))



    We simplified constraint (25) using rules (III), (IV), (IDP_CONSTANT_FOLD), (DELETE_TRIVIAL_REDUCESTO), (IDP_BOOLEAN) which results in the following new constraint:

    (26)    (>(+(i48[6], 1), 1)=TRUE∧<=(-(+(i48[6], 1), 2), 1)=TRUE∧>(+(+(i33[6], 1), 1), 0)=TRUE ⇒ COND_LOAD416(TRUE, +(i48[6], 1), +(i33[6], 1))≥NonInfC∧COND_LOAD416(TRUE, +(i48[6], 1), +(i33[6], 1))≥LOAD583(+(i48[6], 1), +(i33[6], 1), -(+(i48[6], 1), 2), 0)∧(UIncreasing(LOAD583(i36[1], i33[1], -(i36[1], 2), 0)), ≥))



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

    (27)    (i48[6] + [-1] ≥ 0∧[2] + [-1]i48[6] ≥ 0∧i33[6] + [1] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[1], i33[1], -(i36[1], 2), 0)), ≥)∧[(-1)Bound*bni_42] + [bni_42]i48[6] ≥ 0∧[1 + (-1)bso_43] ≥ 0)



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

    (28)    (i48[6] + [-1] ≥ 0∧[2] + [-1]i48[6] ≥ 0∧i33[6] + [1] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[1], i33[1], -(i36[1], 2), 0)), ≥)∧[(-1)Bound*bni_42] + [bni_42]i48[6] ≥ 0∧[1 + (-1)bso_43] ≥ 0)



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

    (29)    (i48[6] + [-1] ≥ 0∧[2] + [-1]i48[6] ≥ 0∧i33[6] + [1] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[1], i33[1], -(i36[1], 2), 0)), ≥)∧[(-1)Bound*bni_42] + [bni_42]i48[6] ≥ 0∧[1 + (-1)bso_43] ≥ 0)



    We simplified constraint (29) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (30)    (i48[6] ≥ 0∧[1] + [-1]i48[6] ≥ 0∧i33[6] + [1] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[1], i33[1], -(i36[1], 2), 0)), ≥)∧[(-1)Bound*bni_42 + bni_42] + [bni_42]i48[6] ≥ 0∧[1 + (-1)bso_43] ≥ 0)



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

    (31)    (i48[6] ≥ 0∧[1] + [-1]i48[6] ≥ 0∧i33[6] + [1] ≥ 0∧i33[6] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[1], i33[1], -(i36[1], 2), 0)), ≥)∧[(-1)Bound*bni_42 + bni_42] + [bni_42]i48[6] ≥ 0∧[1 + (-1)bso_43] ≥ 0)


    (32)    (i48[6] ≥ 0∧[1] + [-1]i48[6] ≥ 0∧[-1]i33[6] + [1] ≥ 0∧i33[6] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[1], i33[1], -(i36[1], 2), 0)), ≥)∧[(-1)Bound*bni_42 + bni_42] + [bni_42]i48[6] ≥ 0∧[1 + (-1)bso_43] ≥ 0)



  • We consider the chain LOAD583(i36[7], i33[7], i50[7], i48[7]) → COND_LOAD5832(&&(&&(<=(i50[7], 1), >(+(i33[7], 1), 0)), >(+(i48[7], 1), 0)), i36[7], i33[7], i50[7], i48[7]), COND_LOAD5832(TRUE, i36[8], i33[8], i50[8], i48[8]) → LOAD416(+(i48[8], 1), +(i33[8], 1)), LOAD416(i36[0], i33[0]) → COND_LOAD416(>(i36[0], 1), i36[0], i33[0]), COND_LOAD416(TRUE, i36[1], i33[1]) → LOAD583(i36[1], i33[1], -(i36[1], 2), 0), LOAD583(i36[2], i33[2], i51[2], i48[2]) → COND_LOAD583(&&(>(i51[2], 1), >(+(i48[2], 1), 0)), i36[2], i33[2], i51[2], i48[2]), COND_LOAD583(TRUE, i36[3], i33[3], i51[3], i48[3]) → LOAD583(i36[3], i33[3], -(i51[3], 2), +(i48[3], 1)) which results in the following constraint:

    (33)    (i50[7]=i50[8]∧i33[7]=i33[8]∧i36[7]=i36[8]∧i48[7]=i48[8]∧&&(&&(<=(i50[7], 1), >(+(i33[7], 1), 0)), >(+(i48[7], 1), 0))=TRUE∧+(i48[8], 1)=i36[0]∧+(i33[8], 1)=i33[0]∧i33[0]=i33[1]∧>(i36[0], 1)=TRUE∧i36[0]=i36[1]∧0=i48[2]∧-(i36[1], 2)=i51[2]∧i33[1]=i33[2]∧i36[1]=i36[2]∧i36[2]=i36[3]∧i51[2]=i51[3]∧i33[2]=i33[3]∧i48[2]=i48[3]∧&&(>(i51[2], 1), >(+(i48[2], 1), 0))=TRUE ⇒ COND_LOAD416(TRUE, i36[1], i33[1])≥NonInfC∧COND_LOAD416(TRUE, i36[1], i33[1])≥LOAD583(i36[1], i33[1], -(i36[1], 2), 0)∧(UIncreasing(LOAD583(i36[1], i33[1], -(i36[1], 2), 0)), ≥))



    We simplified constraint (33) using rules (III), (IV), (IDP_CONSTANT_FOLD), (DELETE_TRIVIAL_REDUCESTO), (IDP_BOOLEAN) which results in the following new constraint:

    (34)    (>(+(i48[7], 1), 1)=TRUE∧>(+(i48[7], 1), 0)=TRUE∧>(-(+(i48[7], 1), 2), 1)=TRUE∧<=(i50[7], 1)=TRUE∧>(+(i33[7], 1), 0)=TRUE ⇒ COND_LOAD416(TRUE, +(i48[7], 1), +(i33[7], 1))≥NonInfC∧COND_LOAD416(TRUE, +(i48[7], 1), +(i33[7], 1))≥LOAD583(+(i48[7], 1), +(i33[7], 1), -(+(i48[7], 1), 2), 0)∧(UIncreasing(LOAD583(i36[1], i33[1], -(i36[1], 2), 0)), ≥))



    We simplified constraint (34) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (35)    (i48[7] + [-1] ≥ 0∧i48[7] ≥ 0∧i48[7] + [-3] ≥ 0∧[1] + [-1]i50[7] ≥ 0∧i33[7] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[1], i33[1], -(i36[1], 2), 0)), ≥)∧[(-1)Bound*bni_42] + [bni_42]i48[7] ≥ 0∧[1 + (-1)bso_43] ≥ 0)



    We simplified constraint (35) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (36)    (i48[7] + [-1] ≥ 0∧i48[7] ≥ 0∧i48[7] + [-3] ≥ 0∧[1] + [-1]i50[7] ≥ 0∧i33[7] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[1], i33[1], -(i36[1], 2), 0)), ≥)∧[(-1)Bound*bni_42] + [bni_42]i48[7] ≥ 0∧[1 + (-1)bso_43] ≥ 0)



    We simplified constraint (36) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (37)    (i48[7] + [-1] ≥ 0∧i48[7] ≥ 0∧i48[7] + [-3] ≥ 0∧[1] + [-1]i50[7] ≥ 0∧i33[7] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[1], i33[1], -(i36[1], 2), 0)), ≥)∧[(-1)Bound*bni_42] + [bni_42]i48[7] ≥ 0∧[1 + (-1)bso_43] ≥ 0)



    We simplified constraint (37) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (38)    (i48[7] ≥ 0∧[1] + i48[7] ≥ 0∧[-2] + i48[7] ≥ 0∧[1] + [-1]i50[7] ≥ 0∧i33[7] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[1], i33[1], -(i36[1], 2), 0)), ≥)∧[(-1)Bound*bni_42 + bni_42] + [bni_42]i48[7] ≥ 0∧[1 + (-1)bso_43] ≥ 0)



    We simplified constraint (38) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (39)    ([2] + i48[7] ≥ 0∧[3] + i48[7] ≥ 0∧i48[7] ≥ 0∧[1] + [-1]i50[7] ≥ 0∧i33[7] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[1], i33[1], -(i36[1], 2), 0)), ≥)∧[(-1)Bound*bni_42 + (3)bni_42] + [bni_42]i48[7] ≥ 0∧[1 + (-1)bso_43] ≥ 0)



    We simplified constraint (39) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (40)    ([2] + i48[7] ≥ 0∧[3] + i48[7] ≥ 0∧i48[7] ≥ 0∧i33[7] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[1], i33[1], -(i36[1], 2), 0)), ≥)∧[(-1)Bound*bni_42 + (3)bni_42] + [bni_42]i48[7] ≥ 0∧[1 + (-1)bso_43] ≥ 0)



  • We consider the chain LOAD583(i36[7], i33[7], i50[7], i48[7]) → COND_LOAD5832(&&(&&(<=(i50[7], 1), >(+(i33[7], 1), 0)), >(+(i48[7], 1), 0)), i36[7], i33[7], i50[7], i48[7]), COND_LOAD5832(TRUE, i36[8], i33[8], i50[8], i48[8]) → LOAD416(+(i48[8], 1), +(i33[8], 1)), LOAD416(i36[0], i33[0]) → COND_LOAD416(>(i36[0], 1), i36[0], i33[0]), COND_LOAD416(TRUE, i36[1], i33[1]) → LOAD583(i36[1], i33[1], -(i36[1], 2), 0), LOAD583(i36[4], i33[4], i51[4], i48[4]) → COND_LOAD5831(&&(>(i51[4], 0), <=(i51[4], 1)), i36[4], i33[4], i51[4], i48[4]), COND_LOAD5831(TRUE, i36[5], i33[5], i51[5], i48[5]) → LOAD594(i36[5], i33[5], i48[5]) which results in the following constraint:

    (41)    (i50[7]=i50[8]∧i33[7]=i33[8]∧i36[7]=i36[8]∧i48[7]=i48[8]∧&&(&&(<=(i50[7], 1), >(+(i33[7], 1), 0)), >(+(i48[7], 1), 0))=TRUE∧+(i48[8], 1)=i36[0]∧+(i33[8], 1)=i33[0]∧i33[0]=i33[1]∧>(i36[0], 1)=TRUE∧i36[0]=i36[1]∧i33[1]=i33[4]∧i36[1]=i36[4]∧0=i48[4]∧-(i36[1], 2)=i51[4]∧&&(>(i51[4], 0), <=(i51[4], 1))=TRUE∧i36[4]=i36[5]∧i51[4]=i51[5]∧i48[4]=i48[5]∧i33[4]=i33[5] ⇒ COND_LOAD416(TRUE, i36[1], i33[1])≥NonInfC∧COND_LOAD416(TRUE, i36[1], i33[1])≥LOAD583(i36[1], i33[1], -(i36[1], 2), 0)∧(UIncreasing(LOAD583(i36[1], i33[1], -(i36[1], 2), 0)), ≥))



    We simplified constraint (41) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (42)    (>(+(i48[7], 1), 1)=TRUE∧>(+(i48[7], 1), 0)=TRUE∧>(-(+(i48[7], 1), 2), 0)=TRUE∧<=(-(+(i48[7], 1), 2), 1)=TRUE∧<=(i50[7], 1)=TRUE∧>(+(i33[7], 1), 0)=TRUE ⇒ COND_LOAD416(TRUE, +(i48[7], 1), +(i33[7], 1))≥NonInfC∧COND_LOAD416(TRUE, +(i48[7], 1), +(i33[7], 1))≥LOAD583(+(i48[7], 1), +(i33[7], 1), -(+(i48[7], 1), 2), 0)∧(UIncreasing(LOAD583(i36[1], i33[1], -(i36[1], 2), 0)), ≥))



    We simplified constraint (42) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (43)    (i48[7] + [-1] ≥ 0∧i48[7] ≥ 0∧i48[7] + [-2] ≥ 0∧[2] + [-1]i48[7] ≥ 0∧[1] + [-1]i50[7] ≥ 0∧i33[7] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[1], i33[1], -(i36[1], 2), 0)), ≥)∧[(-1)Bound*bni_42] + [bni_42]i48[7] ≥ 0∧[1 + (-1)bso_43] ≥ 0)



    We simplified constraint (43) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (44)    (i48[7] + [-1] ≥ 0∧i48[7] ≥ 0∧i48[7] + [-2] ≥ 0∧[2] + [-1]i48[7] ≥ 0∧[1] + [-1]i50[7] ≥ 0∧i33[7] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[1], i33[1], -(i36[1], 2), 0)), ≥)∧[(-1)Bound*bni_42] + [bni_42]i48[7] ≥ 0∧[1 + (-1)bso_43] ≥ 0)



    We simplified constraint (44) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (45)    (i48[7] + [-1] ≥ 0∧i48[7] ≥ 0∧i48[7] + [-2] ≥ 0∧[2] + [-1]i48[7] ≥ 0∧[1] + [-1]i50[7] ≥ 0∧i33[7] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[1], i33[1], -(i36[1], 2), 0)), ≥)∧[(-1)Bound*bni_42] + [bni_42]i48[7] ≥ 0∧[1 + (-1)bso_43] ≥ 0)



    We simplified constraint (45) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (46)    (i48[7] ≥ 0∧[1] + i48[7] ≥ 0∧[-1] + i48[7] ≥ 0∧[1] + [-1]i48[7] ≥ 0∧[1] + [-1]i50[7] ≥ 0∧i33[7] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[1], i33[1], -(i36[1], 2), 0)), ≥)∧[(-1)Bound*bni_42 + bni_42] + [bni_42]i48[7] ≥ 0∧[1 + (-1)bso_43] ≥ 0)



    We simplified constraint (46) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (47)    ([1] + i48[7] ≥ 0∧[2] + i48[7] ≥ 0∧i48[7] ≥ 0∧[-1]i48[7] ≥ 0∧[1] + [-1]i50[7] ≥ 0∧i33[7] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[1], i33[1], -(i36[1], 2), 0)), ≥)∧[(-1)Bound*bni_42 + (2)bni_42] + [bni_42]i48[7] ≥ 0∧[1 + (-1)bso_43] ≥ 0)



    We simplified constraint (47) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (48)    ([1] ≥ 0∧[2] ≥ 0∧0 ≥ 0∧0 ≥ 0∧[1] + [-1]i50[7] ≥ 0∧i33[7] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[1], i33[1], -(i36[1], 2), 0)), ≥)∧[(-1)Bound*bni_42 + (2)bni_42] ≥ 0∧[1 + (-1)bso_43] ≥ 0)



    We simplified constraint (48) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (49)    ([1] ≥ 0∧[2] ≥ 0∧0 ≥ 0∧0 ≥ 0∧i33[7] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[1], i33[1], -(i36[1], 2), 0)), ≥)∧[(-1)Bound*bni_42 + (2)bni_42] ≥ 0∧[1 + (-1)bso_43] ≥ 0)



    We simplified constraint (49) using rule (IDP_POLY_GCD) which results in the following new constraint:

    (50)    ([1] ≥ 0∧0 ≥ 0∧0 ≥ 0∧i33[7] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[1], i33[1], -(i36[1], 2), 0)), ≥)∧[(-1)Bound*bni_42 + (2)bni_42] ≥ 0∧[1 + (-1)bso_43] ≥ 0)



  • We consider the chain LOAD583(i36[7], i33[7], i50[7], i48[7]) → COND_LOAD5832(&&(&&(<=(i50[7], 1), >(+(i33[7], 1), 0)), >(+(i48[7], 1), 0)), i36[7], i33[7], i50[7], i48[7]), COND_LOAD5832(TRUE, i36[8], i33[8], i50[8], i48[8]) → LOAD416(+(i48[8], 1), +(i33[8], 1)), LOAD416(i36[0], i33[0]) → COND_LOAD416(>(i36[0], 1), i36[0], i33[0]), COND_LOAD416(TRUE, i36[1], i33[1]) → LOAD583(i36[1], i33[1], -(i36[1], 2), 0), LOAD583(i36[7], i33[7], i50[7], i48[7]) → COND_LOAD5832(&&(&&(<=(i50[7], 1), >(+(i33[7], 1), 0)), >(+(i48[7], 1), 0)), i36[7], i33[7], i50[7], i48[7]), COND_LOAD5832(TRUE, i36[8], i33[8], i50[8], i48[8]) → LOAD416(+(i48[8], 1), +(i33[8], 1)) which results in the following constraint:

    (51)    (i50[7]=i50[8]∧i33[7]=i33[8]∧i36[7]=i36[8]∧i48[7]=i48[8]∧&&(&&(<=(i50[7], 1), >(+(i33[7], 1), 0)), >(+(i48[7], 1), 0))=TRUE∧+(i48[8], 1)=i36[0]∧+(i33[8], 1)=i33[0]∧i33[0]=i33[1]∧>(i36[0], 1)=TRUE∧i36[0]=i36[1]∧-(i36[1], 2)=i50[7]1∧i33[1]=i33[7]1∧0=i48[7]1∧i36[1]=i36[7]1∧i50[7]1=i50[8]1∧i33[7]1=i33[8]1∧i36[7]1=i36[8]1∧i48[7]1=i48[8]1∧&&(&&(<=(i50[7]1, 1), >(+(i33[7]1, 1), 0)), >(+(i48[7]1, 1), 0))=TRUE ⇒ COND_LOAD416(TRUE, i36[1], i33[1])≥NonInfC∧COND_LOAD416(TRUE, i36[1], i33[1])≥LOAD583(i36[1], i33[1], -(i36[1], 2), 0)∧(UIncreasing(LOAD583(i36[1], i33[1], -(i36[1], 2), 0)), ≥))



    We simplified constraint (51) using rules (III), (IV), (IDP_CONSTANT_FOLD), (DELETE_TRIVIAL_REDUCESTO), (IDP_BOOLEAN) which results in the following new constraint:

    (52)    (>(+(i48[7], 1), 1)=TRUE∧>(+(i48[7], 1), 0)=TRUE∧<=(i50[7], 1)=TRUE∧>(+(i33[7], 1), 0)=TRUE∧<=(-(+(i48[7], 1), 2), 1)=TRUE∧>(+(+(i33[7], 1), 1), 0)=TRUE ⇒ COND_LOAD416(TRUE, +(i48[7], 1), +(i33[7], 1))≥NonInfC∧COND_LOAD416(TRUE, +(i48[7], 1), +(i33[7], 1))≥LOAD583(+(i48[7], 1), +(i33[7], 1), -(+(i48[7], 1), 2), 0)∧(UIncreasing(LOAD583(i36[1], i33[1], -(i36[1], 2), 0)), ≥))



    We simplified constraint (52) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (53)    (i48[7] + [-1] ≥ 0∧i48[7] ≥ 0∧[1] + [-1]i50[7] ≥ 0∧i33[7] ≥ 0∧[2] + [-1]i48[7] ≥ 0∧i33[7] + [1] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[1], i33[1], -(i36[1], 2), 0)), ≥)∧[(-1)Bound*bni_42] + [bni_42]i48[7] ≥ 0∧[1 + (-1)bso_43] ≥ 0)



    We simplified constraint (53) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (54)    (i48[7] + [-1] ≥ 0∧i48[7] ≥ 0∧[1] + [-1]i50[7] ≥ 0∧i33[7] ≥ 0∧[2] + [-1]i48[7] ≥ 0∧i33[7] + [1] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[1], i33[1], -(i36[1], 2), 0)), ≥)∧[(-1)Bound*bni_42] + [bni_42]i48[7] ≥ 0∧[1 + (-1)bso_43] ≥ 0)



    We simplified constraint (54) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (55)    (i48[7] + [-1] ≥ 0∧i48[7] ≥ 0∧[1] + [-1]i50[7] ≥ 0∧i33[7] ≥ 0∧[2] + [-1]i48[7] ≥ 0∧i33[7] + [1] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[1], i33[1], -(i36[1], 2), 0)), ≥)∧[(-1)Bound*bni_42] + [bni_42]i48[7] ≥ 0∧[1 + (-1)bso_43] ≥ 0)



    We simplified constraint (55) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (56)    (i48[7] ≥ 0∧[1] + i48[7] ≥ 0∧[1] + [-1]i50[7] ≥ 0∧i33[7] ≥ 0∧[1] + [-1]i48[7] ≥ 0∧i33[7] + [1] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[1], i33[1], -(i36[1], 2), 0)), ≥)∧[(-1)Bound*bni_42 + bni_42] + [bni_42]i48[7] ≥ 0∧[1 + (-1)bso_43] ≥ 0)



    We simplified constraint (56) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (57)    (i48[7] ≥ 0∧[1] + i48[7] ≥ 0∧i33[7] ≥ 0∧[1] + [-1]i48[7] ≥ 0∧i33[7] + [1] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[1], i33[1], -(i36[1], 2), 0)), ≥)∧[(-1)Bound*bni_42 + bni_42] + [bni_42]i48[7] ≥ 0∧[1 + (-1)bso_43] ≥ 0)







For Pair LOAD583(i36, i33, i51, i48) → COND_LOAD583(&&(>(i51, 1), >(+(i48, 1), 0)), i36, i33, i51, i48) the following chains were created:
  • We consider the chain LOAD583(i36[2], i33[2], i51[2], i48[2]) → COND_LOAD583(&&(>(i51[2], 1), >(+(i48[2], 1), 0)), i36[2], i33[2], i51[2], i48[2]), COND_LOAD583(TRUE, i36[3], i33[3], i51[3], i48[3]) → LOAD583(i36[3], i33[3], -(i51[3], 2), +(i48[3], 1)) which results in the following constraint:

    (58)    (i36[2]=i36[3]∧i51[2]=i51[3]∧i33[2]=i33[3]∧i48[2]=i48[3]∧&&(>(i51[2], 1), >(+(i48[2], 1), 0))=TRUE ⇒ LOAD583(i36[2], i33[2], i51[2], i48[2])≥NonInfC∧LOAD583(i36[2], i33[2], i51[2], i48[2])≥COND_LOAD583(&&(>(i51[2], 1), >(+(i48[2], 1), 0)), i36[2], i33[2], i51[2], i48[2])∧(UIncreasing(COND_LOAD583(&&(>(i51[2], 1), >(+(i48[2], 1), 0)), i36[2], i33[2], i51[2], i48[2])), ≥))



    We simplified constraint (58) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (59)    (>(i51[2], 1)=TRUE∧>(+(i48[2], 1), 0)=TRUE ⇒ LOAD583(i36[2], i33[2], i51[2], i48[2])≥NonInfC∧LOAD583(i36[2], i33[2], i51[2], i48[2])≥COND_LOAD583(&&(>(i51[2], 1), >(+(i48[2], 1), 0)), i36[2], i33[2], i51[2], i48[2])∧(UIncreasing(COND_LOAD583(&&(>(i51[2], 1), >(+(i48[2], 1), 0)), i36[2], i33[2], i51[2], i48[2])), ≥))



    We simplified constraint (59) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (60)    (i51[2] + [-2] ≥ 0∧i48[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD583(&&(>(i51[2], 1), >(+(i48[2], 1), 0)), i36[2], i33[2], i51[2], i48[2])), ≥)∧[(-1)Bound*bni_44] + [bni_44]i48[2] + [bni_44]i51[2] ≥ 0∧[1 + (-1)bso_45] ≥ 0)



    We simplified constraint (60) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (61)    (i51[2] + [-2] ≥ 0∧i48[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD583(&&(>(i51[2], 1), >(+(i48[2], 1), 0)), i36[2], i33[2], i51[2], i48[2])), ≥)∧[(-1)Bound*bni_44] + [bni_44]i48[2] + [bni_44]i51[2] ≥ 0∧[1 + (-1)bso_45] ≥ 0)



    We simplified constraint (61) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (62)    (i51[2] + [-2] ≥ 0∧i48[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD583(&&(>(i51[2], 1), >(+(i48[2], 1), 0)), i36[2], i33[2], i51[2], i48[2])), ≥)∧[(-1)Bound*bni_44] + [bni_44]i48[2] + [bni_44]i51[2] ≥ 0∧[1 + (-1)bso_45] ≥ 0)



    We simplified constraint (62) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

    (63)    (i51[2] + [-2] ≥ 0∧i48[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD583(&&(>(i51[2], 1), >(+(i48[2], 1), 0)), i36[2], i33[2], i51[2], i48[2])), ≥)∧0 = 0∧0 = 0∧[(-1)Bound*bni_44] + [bni_44]i48[2] + [bni_44]i51[2] ≥ 0∧0 = 0∧0 = 0∧[1 + (-1)bso_45] ≥ 0)



    We simplified constraint (63) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (64)    (i51[2] ≥ 0∧i48[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD583(&&(>(i51[2], 1), >(+(i48[2], 1), 0)), i36[2], i33[2], i51[2], i48[2])), ≥)∧0 = 0∧0 = 0∧[(-1)Bound*bni_44 + (2)bni_44] + [bni_44]i48[2] + [bni_44]i51[2] ≥ 0∧0 = 0∧0 = 0∧[1 + (-1)bso_45] ≥ 0)







For Pair COND_LOAD583(TRUE, i36, i33, i51, i48) → LOAD583(i36, i33, -(i51, 2), +(i48, 1)) the following chains were created:
  • We consider the chain LOAD416(i36[0], i33[0]) → COND_LOAD416(>(i36[0], 1), i36[0], i33[0]), COND_LOAD416(TRUE, i36[1], i33[1]) → LOAD583(i36[1], i33[1], -(i36[1], 2), 0), LOAD583(i36[2], i33[2], i51[2], i48[2]) → COND_LOAD583(&&(>(i51[2], 1), >(+(i48[2], 1), 0)), i36[2], i33[2], i51[2], i48[2]), COND_LOAD583(TRUE, i36[3], i33[3], i51[3], i48[3]) → LOAD583(i36[3], i33[3], -(i51[3], 2), +(i48[3], 1)), LOAD583(i36[2], i33[2], i51[2], i48[2]) → COND_LOAD583(&&(>(i51[2], 1), >(+(i48[2], 1), 0)), i36[2], i33[2], i51[2], i48[2]), COND_LOAD583(TRUE, i36[3], i33[3], i51[3], i48[3]) → LOAD583(i36[3], i33[3], -(i51[3], 2), +(i48[3], 1)) which results in the following constraint:

    (65)    (i33[0]=i33[1]∧>(i36[0], 1)=TRUE∧i36[0]=i36[1]∧0=i48[2]∧-(i36[1], 2)=i51[2]∧i33[1]=i33[2]∧i36[1]=i36[2]∧i36[2]=i36[3]∧i51[2]=i51[3]∧i33[2]=i33[3]∧i48[2]=i48[3]∧&&(>(i51[2], 1), >(+(i48[2], 1), 0))=TRUE∧+(i48[3], 1)=i48[2]1∧-(i51[3], 2)=i51[2]1∧i33[3]=i33[2]1∧i36[3]=i36[2]1∧i36[2]1=i36[3]1∧i51[2]1=i51[3]1∧i33[2]1=i33[3]1∧i48[2]1=i48[3]1∧&&(>(i51[2]1, 1), >(+(i48[2]1, 1), 0))=TRUE ⇒ COND_LOAD583(TRUE, i36[3], i33[3], i51[3], i48[3])≥NonInfC∧COND_LOAD583(TRUE, i36[3], i33[3], i51[3], i48[3])≥LOAD583(i36[3], i33[3], -(i51[3], 2), +(i48[3], 1))∧(UIncreasing(LOAD583(i36[3], i33[3], -(i51[3], 2), +(i48[3], 1))), ≥))



    We simplified constraint (65) using rules (III), (IV), (IDP_CONSTANT_FOLD), (DELETE_TRIVIAL_REDUCESTO), (IDP_BOOLEAN) which results in the following new constraint:

    (66)    (>(i36[0], 1)=TRUE∧>(-(i36[0], 2), 1)=TRUE∧>(-(-(i36[0], 2), 2), 1)=TRUE ⇒ COND_LOAD583(TRUE, i36[0], i33[0], -(i36[0], 2), 0)≥NonInfC∧COND_LOAD583(TRUE, i36[0], i33[0], -(i36[0], 2), 0)≥LOAD583(i36[0], i33[0], -(-(i36[0], 2), 2), +(0, 1))∧(UIncreasing(LOAD583(i36[3], i33[3], -(i51[3], 2), +(i48[3], 1))), ≥))



    We simplified constraint (66) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (67)    (i36[0] + [-2] ≥ 0∧i36[0] + [-4] ≥ 0∧i36[0] + [-6] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[3], i33[3], -(i51[3], 2), +(i48[3], 1))), ≥)∧[(-3)bni_46 + (-1)Bound*bni_46] + [bni_46]i36[0] ≥ 0∧[(-1)bso_47] ≥ 0)



    We simplified constraint (67) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (68)    (i36[0] + [-2] ≥ 0∧i36[0] + [-4] ≥ 0∧i36[0] + [-6] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[3], i33[3], -(i51[3], 2), +(i48[3], 1))), ≥)∧[(-3)bni_46 + (-1)Bound*bni_46] + [bni_46]i36[0] ≥ 0∧[(-1)bso_47] ≥ 0)



    We simplified constraint (68) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (69)    (i36[0] + [-2] ≥ 0∧i36[0] + [-4] ≥ 0∧i36[0] + [-6] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[3], i33[3], -(i51[3], 2), +(i48[3], 1))), ≥)∧[(-3)bni_46 + (-1)Bound*bni_46] + [bni_46]i36[0] ≥ 0∧[(-1)bso_47] ≥ 0)



    We simplified constraint (69) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

    (70)    (i36[0] + [-2] ≥ 0∧i36[0] + [-4] ≥ 0∧i36[0] + [-6] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[3], i33[3], -(i51[3], 2), +(i48[3], 1))), ≥)∧0 = 0∧[(-3)bni_46 + (-1)Bound*bni_46] + [bni_46]i36[0] ≥ 0∧0 = 0∧[(-1)bso_47] ≥ 0)



    We simplified constraint (70) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (71)    (i36[0] ≥ 0∧[-2] + i36[0] ≥ 0∧[-4] + i36[0] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[3], i33[3], -(i51[3], 2), +(i48[3], 1))), ≥)∧0 = 0∧[(-1)bni_46 + (-1)Bound*bni_46] + [bni_46]i36[0] ≥ 0∧0 = 0∧[(-1)bso_47] ≥ 0)



    We simplified constraint (71) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (72)    ([2] + i36[0] ≥ 0∧i36[0] ≥ 0∧[-2] + i36[0] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[3], i33[3], -(i51[3], 2), +(i48[3], 1))), ≥)∧0 = 0∧[bni_46 + (-1)Bound*bni_46] + [bni_46]i36[0] ≥ 0∧0 = 0∧[(-1)bso_47] ≥ 0)



    We simplified constraint (72) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (73)    ([4] + i36[0] ≥ 0∧[2] + i36[0] ≥ 0∧i36[0] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[3], i33[3], -(i51[3], 2), +(i48[3], 1))), ≥)∧0 = 0∧[(3)bni_46 + (-1)Bound*bni_46] + [bni_46]i36[0] ≥ 0∧0 = 0∧[(-1)bso_47] ≥ 0)



  • We consider the chain LOAD416(i36[0], i33[0]) → COND_LOAD416(>(i36[0], 1), i36[0], i33[0]), COND_LOAD416(TRUE, i36[1], i33[1]) → LOAD583(i36[1], i33[1], -(i36[1], 2), 0), LOAD583(i36[2], i33[2], i51[2], i48[2]) → COND_LOAD583(&&(>(i51[2], 1), >(+(i48[2], 1), 0)), i36[2], i33[2], i51[2], i48[2]), COND_LOAD583(TRUE, i36[3], i33[3], i51[3], i48[3]) → LOAD583(i36[3], i33[3], -(i51[3], 2), +(i48[3], 1)), LOAD583(i36[4], i33[4], i51[4], i48[4]) → COND_LOAD5831(&&(>(i51[4], 0), <=(i51[4], 1)), i36[4], i33[4], i51[4], i48[4]), COND_LOAD5831(TRUE, i36[5], i33[5], i51[5], i48[5]) → LOAD594(i36[5], i33[5], i48[5]) which results in the following constraint:

    (74)    (i33[0]=i33[1]∧>(i36[0], 1)=TRUE∧i36[0]=i36[1]∧0=i48[2]∧-(i36[1], 2)=i51[2]∧i33[1]=i33[2]∧i36[1]=i36[2]∧i36[2]=i36[3]∧i51[2]=i51[3]∧i33[2]=i33[3]∧i48[2]=i48[3]∧&&(>(i51[2], 1), >(+(i48[2], 1), 0))=TRUE∧+(i48[3], 1)=i48[4]∧i36[3]=i36[4]∧i33[3]=i33[4]∧-(i51[3], 2)=i51[4]∧&&(>(i51[4], 0), <=(i51[4], 1))=TRUE∧i36[4]=i36[5]∧i51[4]=i51[5]∧i48[4]=i48[5]∧i33[4]=i33[5] ⇒ COND_LOAD583(TRUE, i36[3], i33[3], i51[3], i48[3])≥NonInfC∧COND_LOAD583(TRUE, i36[3], i33[3], i51[3], i48[3])≥LOAD583(i36[3], i33[3], -(i51[3], 2), +(i48[3], 1))∧(UIncreasing(LOAD583(i36[3], i33[3], -(i51[3], 2), +(i48[3], 1))), ≥))



    We simplified constraint (74) using rules (III), (IV), (IDP_CONSTANT_FOLD), (DELETE_TRIVIAL_REDUCESTO), (IDP_BOOLEAN) which results in the following new constraint:

    (75)    (>(i36[0], 1)=TRUE∧>(-(i36[0], 2), 1)=TRUE∧>(-(-(i36[0], 2), 2), 0)=TRUE∧<=(-(-(i36[0], 2), 2), 1)=TRUE ⇒ COND_LOAD583(TRUE, i36[0], i33[0], -(i36[0], 2), 0)≥NonInfC∧COND_LOAD583(TRUE, i36[0], i33[0], -(i36[0], 2), 0)≥LOAD583(i36[0], i33[0], -(-(i36[0], 2), 2), +(0, 1))∧(UIncreasing(LOAD583(i36[3], i33[3], -(i51[3], 2), +(i48[3], 1))), ≥))



    We simplified constraint (75) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (76)    (i36[0] + [-2] ≥ 0∧i36[0] + [-4] ≥ 0∧i36[0] + [-5] ≥ 0∧[5] + [-1]i36[0] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[3], i33[3], -(i51[3], 2), +(i48[3], 1))), ≥)∧[(-3)bni_46 + (-1)Bound*bni_46] + [bni_46]i36[0] ≥ 0∧[(-1)bso_47] ≥ 0)



    We simplified constraint (76) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (77)    (i36[0] + [-2] ≥ 0∧i36[0] + [-4] ≥ 0∧i36[0] + [-5] ≥ 0∧[5] + [-1]i36[0] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[3], i33[3], -(i51[3], 2), +(i48[3], 1))), ≥)∧[(-3)bni_46 + (-1)Bound*bni_46] + [bni_46]i36[0] ≥ 0∧[(-1)bso_47] ≥ 0)



    We simplified constraint (77) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (78)    (i36[0] + [-2] ≥ 0∧i36[0] + [-4] ≥ 0∧i36[0] + [-5] ≥ 0∧[5] + [-1]i36[0] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[3], i33[3], -(i51[3], 2), +(i48[3], 1))), ≥)∧[(-3)bni_46 + (-1)Bound*bni_46] + [bni_46]i36[0] ≥ 0∧[(-1)bso_47] ≥ 0)



    We simplified constraint (78) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

    (79)    (i36[0] + [-2] ≥ 0∧i36[0] + [-4] ≥ 0∧i36[0] + [-5] ≥ 0∧[5] + [-1]i36[0] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[3], i33[3], -(i51[3], 2), +(i48[3], 1))), ≥)∧0 = 0∧[(-3)bni_46 + (-1)Bound*bni_46] + [bni_46]i36[0] ≥ 0∧0 = 0∧[(-1)bso_47] ≥ 0)



    We simplified constraint (79) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (80)    (i36[0] ≥ 0∧[-2] + i36[0] ≥ 0∧[-3] + i36[0] ≥ 0∧[3] + [-1]i36[0] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[3], i33[3], -(i51[3], 2), +(i48[3], 1))), ≥)∧0 = 0∧[(-1)bni_46 + (-1)Bound*bni_46] + [bni_46]i36[0] ≥ 0∧0 = 0∧[(-1)bso_47] ≥ 0)



    We simplified constraint (80) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (81)    ([2] + i36[0] ≥ 0∧i36[0] ≥ 0∧[-1] + i36[0] ≥ 0∧[1] + [-1]i36[0] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[3], i33[3], -(i51[3], 2), +(i48[3], 1))), ≥)∧0 = 0∧[bni_46 + (-1)Bound*bni_46] + [bni_46]i36[0] ≥ 0∧0 = 0∧[(-1)bso_47] ≥ 0)



    We simplified constraint (81) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (82)    ([3] + i36[0] ≥ 0∧[1] + i36[0] ≥ 0∧i36[0] ≥ 0∧[-1]i36[0] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[3], i33[3], -(i51[3], 2), +(i48[3], 1))), ≥)∧0 = 0∧[(2)bni_46 + (-1)Bound*bni_46] + [bni_46]i36[0] ≥ 0∧0 = 0∧[(-1)bso_47] ≥ 0)



    We simplified constraint (82) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (83)    ([3] ≥ 0∧[1] ≥ 0∧0 ≥ 0∧0 ≥ 0 ⇒ (UIncreasing(LOAD583(i36[3], i33[3], -(i51[3], 2), +(i48[3], 1))), ≥)∧0 = 0∧[(2)bni_46 + (-1)Bound*bni_46] ≥ 0∧0 = 0∧[(-1)bso_47] ≥ 0)



    We simplified constraint (83) using rule (IDP_POLY_GCD) which results in the following new constraint:

    (84)    ([1] ≥ 0∧0 ≥ 0∧0 ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[3], i33[3], -(i51[3], 2), +(i48[3], 1))), ≥)∧0 = 0∧[(2)bni_46 + (-1)Bound*bni_46] ≥ 0∧0 = 0∧[(-1)bso_47] ≥ 0)



  • We consider the chain LOAD416(i36[0], i33[0]) → COND_LOAD416(>(i36[0], 1), i36[0], i33[0]), COND_LOAD416(TRUE, i36[1], i33[1]) → LOAD583(i36[1], i33[1], -(i36[1], 2), 0), LOAD583(i36[2], i33[2], i51[2], i48[2]) → COND_LOAD583(&&(>(i51[2], 1), >(+(i48[2], 1), 0)), i36[2], i33[2], i51[2], i48[2]), COND_LOAD583(TRUE, i36[3], i33[3], i51[3], i48[3]) → LOAD583(i36[3], i33[3], -(i51[3], 2), +(i48[3], 1)), LOAD583(i36[7], i33[7], i50[7], i48[7]) → COND_LOAD5832(&&(&&(<=(i50[7], 1), >(+(i33[7], 1), 0)), >(+(i48[7], 1), 0)), i36[7], i33[7], i50[7], i48[7]), COND_LOAD5832(TRUE, i36[8], i33[8], i50[8], i48[8]) → LOAD416(+(i48[8], 1), +(i33[8], 1)) which results in the following constraint:

    (85)    (i33[0]=i33[1]∧>(i36[0], 1)=TRUE∧i36[0]=i36[1]∧0=i48[2]∧-(i36[1], 2)=i51[2]∧i33[1]=i33[2]∧i36[1]=i36[2]∧i36[2]=i36[3]∧i51[2]=i51[3]∧i33[2]=i33[3]∧i48[2]=i48[3]∧&&(>(i51[2], 1), >(+(i48[2], 1), 0))=TRUE∧+(i48[3], 1)=i48[7]∧-(i51[3], 2)=i50[7]∧i36[3]=i36[7]∧i33[3]=i33[7]∧i50[7]=i50[8]∧i33[7]=i33[8]∧i36[7]=i36[8]∧i48[7]=i48[8]∧&&(&&(<=(i50[7], 1), >(+(i33[7], 1), 0)), >(+(i48[7], 1), 0))=TRUE ⇒ COND_LOAD583(TRUE, i36[3], i33[3], i51[3], i48[3])≥NonInfC∧COND_LOAD583(TRUE, i36[3], i33[3], i51[3], i48[3])≥LOAD583(i36[3], i33[3], -(i51[3], 2), +(i48[3], 1))∧(UIncreasing(LOAD583(i36[3], i33[3], -(i51[3], 2), +(i48[3], 1))), ≥))



    We simplified constraint (85) using rules (III), (IV), (IDP_CONSTANT_FOLD), (DELETE_TRIVIAL_REDUCESTO), (IDP_BOOLEAN) which results in the following new constraint:

    (86)    (>(i36[0], 1)=TRUE∧>(-(i36[0], 2), 1)=TRUE∧<=(-(-(i36[0], 2), 2), 1)=TRUE∧>(+(i33[7], 1), 0)=TRUE ⇒ COND_LOAD583(TRUE, i36[0], i33[7], -(i36[0], 2), 0)≥NonInfC∧COND_LOAD583(TRUE, i36[0], i33[7], -(i36[0], 2), 0)≥LOAD583(i36[0], i33[7], -(-(i36[0], 2), 2), +(0, 1))∧(UIncreasing(LOAD583(i36[3], i33[3], -(i51[3], 2), +(i48[3], 1))), ≥))



    We simplified constraint (86) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (87)    (i36[0] + [-2] ≥ 0∧i36[0] + [-4] ≥ 0∧[5] + [-1]i36[0] ≥ 0∧i33[7] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[3], i33[3], -(i51[3], 2), +(i48[3], 1))), ≥)∧[(-3)bni_46 + (-1)Bound*bni_46] + [bni_46]i36[0] ≥ 0∧[(-1)bso_47] ≥ 0)



    We simplified constraint (87) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (88)    (i36[0] + [-2] ≥ 0∧i36[0] + [-4] ≥ 0∧[5] + [-1]i36[0] ≥ 0∧i33[7] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[3], i33[3], -(i51[3], 2), +(i48[3], 1))), ≥)∧[(-3)bni_46 + (-1)Bound*bni_46] + [bni_46]i36[0] ≥ 0∧[(-1)bso_47] ≥ 0)



    We simplified constraint (88) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (89)    (i36[0] + [-2] ≥ 0∧i36[0] + [-4] ≥ 0∧[5] + [-1]i36[0] ≥ 0∧i33[7] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[3], i33[3], -(i51[3], 2), +(i48[3], 1))), ≥)∧[(-3)bni_46 + (-1)Bound*bni_46] + [bni_46]i36[0] ≥ 0∧[(-1)bso_47] ≥ 0)



    We simplified constraint (89) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (90)    (i36[0] ≥ 0∧[-2] + i36[0] ≥ 0∧[3] + [-1]i36[0] ≥ 0∧i33[7] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[3], i33[3], -(i51[3], 2), +(i48[3], 1))), ≥)∧[(-1)bni_46 + (-1)Bound*bni_46] + [bni_46]i36[0] ≥ 0∧[(-1)bso_47] ≥ 0)



    We simplified constraint (90) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (91)    ([2] + i36[0] ≥ 0∧i36[0] ≥ 0∧[1] + [-1]i36[0] ≥ 0∧i33[7] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[3], i33[3], -(i51[3], 2), +(i48[3], 1))), ≥)∧[bni_46 + (-1)Bound*bni_46] + [bni_46]i36[0] ≥ 0∧[(-1)bso_47] ≥ 0)



  • We consider the chain LOAD583(i36[2], i33[2], i51[2], i48[2]) → COND_LOAD583(&&(>(i51[2], 1), >(+(i48[2], 1), 0)), i36[2], i33[2], i51[2], i48[2]), COND_LOAD583(TRUE, i36[3], i33[3], i51[3], i48[3]) → LOAD583(i36[3], i33[3], -(i51[3], 2), +(i48[3], 1)), LOAD583(i36[2], i33[2], i51[2], i48[2]) → COND_LOAD583(&&(>(i51[2], 1), >(+(i48[2], 1), 0)), i36[2], i33[2], i51[2], i48[2]), COND_LOAD583(TRUE, i36[3], i33[3], i51[3], i48[3]) → LOAD583(i36[3], i33[3], -(i51[3], 2), +(i48[3], 1)), LOAD583(i36[2], i33[2], i51[2], i48[2]) → COND_LOAD583(&&(>(i51[2], 1), >(+(i48[2], 1), 0)), i36[2], i33[2], i51[2], i48[2]), COND_LOAD583(TRUE, i36[3], i33[3], i51[3], i48[3]) → LOAD583(i36[3], i33[3], -(i51[3], 2), +(i48[3], 1)) which results in the following constraint:

    (92)    (i36[2]=i36[3]∧i51[2]=i51[3]∧i33[2]=i33[3]∧i48[2]=i48[3]∧&&(>(i51[2], 1), >(+(i48[2], 1), 0))=TRUE∧+(i48[3], 1)=i48[2]1∧-(i51[3], 2)=i51[2]1∧i33[3]=i33[2]1∧i36[3]=i36[2]1∧i36[2]1=i36[3]1∧i51[2]1=i51[3]1∧i33[2]1=i33[3]1∧i48[2]1=i48[3]1∧&&(>(i51[2]1, 1), >(+(i48[2]1, 1), 0))=TRUE∧+(i48[3]1, 1)=i48[2]2∧-(i51[3]1, 2)=i51[2]2∧i33[3]1=i33[2]2∧i36[3]1=i36[2]2∧i36[2]2=i36[3]2∧i51[2]2=i51[3]2∧i33[2]2=i33[3]2∧i48[2]2=i48[3]2∧&&(>(i51[2]2, 1), >(+(i48[2]2, 1), 0))=TRUE ⇒ COND_LOAD583(TRUE, i36[3]1, i33[3]1, i51[3]1, i48[3]1)≥NonInfC∧COND_LOAD583(TRUE, i36[3]1, i33[3]1, i51[3]1, i48[3]1)≥LOAD583(i36[3]1, i33[3]1, -(i51[3]1, 2), +(i48[3]1, 1))∧(UIncreasing(LOAD583(i36[3]1, i33[3]1, -(i51[3]1, 2), +(i48[3]1, 1))), ≥))



    We simplified constraint (92) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (93)    (>(i51[2], 1)=TRUE∧>(+(i48[2], 1), 0)=TRUE∧>(-(i51[2], 2), 1)=TRUE∧>(+(+(i48[2], 1), 1), 0)=TRUE∧>(-(-(i51[2], 2), 2), 1)=TRUE∧>(+(+(+(i48[2], 1), 1), 1), 0)=TRUE ⇒ COND_LOAD583(TRUE, i36[2], i33[2], -(i51[2], 2), +(i48[2], 1))≥NonInfC∧COND_LOAD583(TRUE, i36[2], i33[2], -(i51[2], 2), +(i48[2], 1))≥LOAD583(i36[2], i33[2], -(-(i51[2], 2), 2), +(+(i48[2], 1), 1))∧(UIncreasing(LOAD583(i36[3]1, i33[3]1, -(i51[3]1, 2), +(i48[3]1, 1))), ≥))



    We simplified constraint (93) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (94)    (i51[2] + [-2] ≥ 0∧i48[2] ≥ 0∧i51[2] + [-4] ≥ 0∧i48[2] + [1] ≥ 0∧i51[2] + [-6] ≥ 0∧i48[2] + [2] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[3]1, i33[3]1, -(i51[3]1, 2), +(i48[3]1, 1))), ≥)∧[(-2)bni_46 + (-1)Bound*bni_46] + [bni_46]i48[2] + [bni_46]i51[2] ≥ 0∧[(-1)bso_47] ≥ 0)



    We simplified constraint (94) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (95)    (i51[2] + [-2] ≥ 0∧i48[2] ≥ 0∧i51[2] + [-4] ≥ 0∧i48[2] + [1] ≥ 0∧i51[2] + [-6] ≥ 0∧i48[2] + [2] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[3]1, i33[3]1, -(i51[3]1, 2), +(i48[3]1, 1))), ≥)∧[(-2)bni_46 + (-1)Bound*bni_46] + [bni_46]i48[2] + [bni_46]i51[2] ≥ 0∧[(-1)bso_47] ≥ 0)



    We simplified constraint (95) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (96)    (i51[2] + [-2] ≥ 0∧i48[2] ≥ 0∧i51[2] + [-4] ≥ 0∧i48[2] + [1] ≥ 0∧i51[2] + [-6] ≥ 0∧i48[2] + [2] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[3]1, i33[3]1, -(i51[3]1, 2), +(i48[3]1, 1))), ≥)∧[(-2)bni_46 + (-1)Bound*bni_46] + [bni_46]i48[2] + [bni_46]i51[2] ≥ 0∧[(-1)bso_47] ≥ 0)



    We simplified constraint (96) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

    (97)    (i51[2] + [-2] ≥ 0∧i48[2] ≥ 0∧i51[2] + [-4] ≥ 0∧i48[2] + [1] ≥ 0∧i51[2] + [-6] ≥ 0∧i48[2] + [2] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[3]1, i33[3]1, -(i51[3]1, 2), +(i48[3]1, 1))), ≥)∧0 = 0∧0 = 0∧[(-2)bni_46 + (-1)Bound*bni_46] + [bni_46]i48[2] + [bni_46]i51[2] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_47] ≥ 0)



    We simplified constraint (97) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (98)    (i51[2] ≥ 0∧i48[2] ≥ 0∧[-2] + i51[2] ≥ 0∧i48[2] + [1] ≥ 0∧[-4] + i51[2] ≥ 0∧i48[2] + [2] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[3]1, i33[3]1, -(i51[3]1, 2), +(i48[3]1, 1))), ≥)∧0 = 0∧0 = 0∧[(-1)Bound*bni_46] + [bni_46]i48[2] + [bni_46]i51[2] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_47] ≥ 0)



    We simplified constraint (98) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (99)    ([2] + i51[2] ≥ 0∧i48[2] ≥ 0∧i51[2] ≥ 0∧i48[2] + [1] ≥ 0∧[-2] + i51[2] ≥ 0∧i48[2] + [2] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[3]1, i33[3]1, -(i51[3]1, 2), +(i48[3]1, 1))), ≥)∧0 = 0∧0 = 0∧[(2)bni_46 + (-1)Bound*bni_46] + [bni_46]i48[2] + [bni_46]i51[2] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_47] ≥ 0)



    We simplified constraint (99) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (100)    ([4] + i51[2] ≥ 0∧i48[2] ≥ 0∧[2] + i51[2] ≥ 0∧i48[2] + [1] ≥ 0∧i51[2] ≥ 0∧i48[2] + [2] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[3]1, i33[3]1, -(i51[3]1, 2), +(i48[3]1, 1))), ≥)∧0 = 0∧0 = 0∧[(4)bni_46 + (-1)Bound*bni_46] + [bni_46]i48[2] + [bni_46]i51[2] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_47] ≥ 0)



    We simplified constraint (100) using rule (IDP_POLY_GCD) which results in the following new constraint:

    (101)    ([4] + i51[2] ≥ 0∧i48[2] ≥ 0∧[2] + i51[2] ≥ 0∧i48[2] + [1] ≥ 0∧i51[2] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[3]1, i33[3]1, -(i51[3]1, 2), +(i48[3]1, 1))), ≥)∧0 = 0∧0 = 0∧[(4)bni_46 + (-1)Bound*bni_46] + [bni_46]i48[2] + [bni_46]i51[2] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_47] ≥ 0)



  • We consider the chain LOAD583(i36[2], i33[2], i51[2], i48[2]) → COND_LOAD583(&&(>(i51[2], 1), >(+(i48[2], 1), 0)), i36[2], i33[2], i51[2], i48[2]), COND_LOAD583(TRUE, i36[3], i33[3], i51[3], i48[3]) → LOAD583(i36[3], i33[3], -(i51[3], 2), +(i48[3], 1)), LOAD583(i36[2], i33[2], i51[2], i48[2]) → COND_LOAD583(&&(>(i51[2], 1), >(+(i48[2], 1), 0)), i36[2], i33[2], i51[2], i48[2]), COND_LOAD583(TRUE, i36[3], i33[3], i51[3], i48[3]) → LOAD583(i36[3], i33[3], -(i51[3], 2), +(i48[3], 1)), LOAD583(i36[4], i33[4], i51[4], i48[4]) → COND_LOAD5831(&&(>(i51[4], 0), <=(i51[4], 1)), i36[4], i33[4], i51[4], i48[4]), COND_LOAD5831(TRUE, i36[5], i33[5], i51[5], i48[5]) → LOAD594(i36[5], i33[5], i48[5]) which results in the following constraint:

    (102)    (i36[2]=i36[3]∧i51[2]=i51[3]∧i33[2]=i33[3]∧i48[2]=i48[3]∧&&(>(i51[2], 1), >(+(i48[2], 1), 0))=TRUE∧+(i48[3], 1)=i48[2]1∧-(i51[3], 2)=i51[2]1∧i33[3]=i33[2]1∧i36[3]=i36[2]1∧i36[2]1=i36[3]1∧i51[2]1=i51[3]1∧i33[2]1=i33[3]1∧i48[2]1=i48[3]1∧&&(>(i51[2]1, 1), >(+(i48[2]1, 1), 0))=TRUE∧+(i48[3]1, 1)=i48[4]∧i36[3]1=i36[4]∧i33[3]1=i33[4]∧-(i51[3]1, 2)=i51[4]∧&&(>(i51[4], 0), <=(i51[4], 1))=TRUE∧i36[4]=i36[5]∧i51[4]=i51[5]∧i48[4]=i48[5]∧i33[4]=i33[5] ⇒ COND_LOAD583(TRUE, i36[3]1, i33[3]1, i51[3]1, i48[3]1)≥NonInfC∧COND_LOAD583(TRUE, i36[3]1, i33[3]1, i51[3]1, i48[3]1)≥LOAD583(i36[3]1, i33[3]1, -(i51[3]1, 2), +(i48[3]1, 1))∧(UIncreasing(LOAD583(i36[3]1, i33[3]1, -(i51[3]1, 2), +(i48[3]1, 1))), ≥))



    We simplified constraint (102) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (103)    (>(i51[2], 1)=TRUE∧>(+(i48[2], 1), 0)=TRUE∧>(-(i51[2], 2), 1)=TRUE∧>(+(+(i48[2], 1), 1), 0)=TRUE∧>(-(-(i51[2], 2), 2), 0)=TRUE∧<=(-(-(i51[2], 2), 2), 1)=TRUE ⇒ COND_LOAD583(TRUE, i36[2], i33[2], -(i51[2], 2), +(i48[2], 1))≥NonInfC∧COND_LOAD583(TRUE, i36[2], i33[2], -(i51[2], 2), +(i48[2], 1))≥LOAD583(i36[2], i33[2], -(-(i51[2], 2), 2), +(+(i48[2], 1), 1))∧(UIncreasing(LOAD583(i36[3]1, i33[3]1, -(i51[3]1, 2), +(i48[3]1, 1))), ≥))



    We simplified constraint (103) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (104)    (i51[2] + [-2] ≥ 0∧i48[2] ≥ 0∧i51[2] + [-4] ≥ 0∧i48[2] + [1] ≥ 0∧i51[2] + [-5] ≥ 0∧[5] + [-1]i51[2] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[3]1, i33[3]1, -(i51[3]1, 2), +(i48[3]1, 1))), ≥)∧[(-2)bni_46 + (-1)Bound*bni_46] + [bni_46]i48[2] + [bni_46]i51[2] ≥ 0∧[(-1)bso_47] ≥ 0)



    We simplified constraint (104) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (105)    (i51[2] + [-2] ≥ 0∧i48[2] ≥ 0∧i51[2] + [-4] ≥ 0∧i48[2] + [1] ≥ 0∧i51[2] + [-5] ≥ 0∧[5] + [-1]i51[2] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[3]1, i33[3]1, -(i51[3]1, 2), +(i48[3]1, 1))), ≥)∧[(-2)bni_46 + (-1)Bound*bni_46] + [bni_46]i48[2] + [bni_46]i51[2] ≥ 0∧[(-1)bso_47] ≥ 0)



    We simplified constraint (105) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (106)    (i51[2] + [-2] ≥ 0∧i48[2] ≥ 0∧i51[2] + [-4] ≥ 0∧i48[2] + [1] ≥ 0∧i51[2] + [-5] ≥ 0∧[5] + [-1]i51[2] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[3]1, i33[3]1, -(i51[3]1, 2), +(i48[3]1, 1))), ≥)∧[(-2)bni_46 + (-1)Bound*bni_46] + [bni_46]i48[2] + [bni_46]i51[2] ≥ 0∧[(-1)bso_47] ≥ 0)



    We simplified constraint (106) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

    (107)    (i51[2] + [-2] ≥ 0∧i48[2] ≥ 0∧i51[2] + [-4] ≥ 0∧i48[2] + [1] ≥ 0∧i51[2] + [-5] ≥ 0∧[5] + [-1]i51[2] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[3]1, i33[3]1, -(i51[3]1, 2), +(i48[3]1, 1))), ≥)∧0 = 0∧0 = 0∧[(-2)bni_46 + (-1)Bound*bni_46] + [bni_46]i48[2] + [bni_46]i51[2] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_47] ≥ 0)



    We simplified constraint (107) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (108)    (i51[2] ≥ 0∧i48[2] ≥ 0∧[-2] + i51[2] ≥ 0∧i48[2] + [1] ≥ 0∧[-3] + i51[2] ≥ 0∧[3] + [-1]i51[2] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[3]1, i33[3]1, -(i51[3]1, 2), +(i48[3]1, 1))), ≥)∧0 = 0∧0 = 0∧[(-1)Bound*bni_46] + [bni_46]i48[2] + [bni_46]i51[2] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_47] ≥ 0)



    We simplified constraint (108) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (109)    ([2] + i51[2] ≥ 0∧i48[2] ≥ 0∧i51[2] ≥ 0∧i48[2] + [1] ≥ 0∧[-1] + i51[2] ≥ 0∧[1] + [-1]i51[2] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[3]1, i33[3]1, -(i51[3]1, 2), +(i48[3]1, 1))), ≥)∧0 = 0∧0 = 0∧[(2)bni_46 + (-1)Bound*bni_46] + [bni_46]i48[2] + [bni_46]i51[2] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_47] ≥ 0)



    We simplified constraint (109) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (110)    ([3] + i51[2] ≥ 0∧i48[2] ≥ 0∧[1] + i51[2] ≥ 0∧i48[2] + [1] ≥ 0∧i51[2] ≥ 0∧[-1]i51[2] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[3]1, i33[3]1, -(i51[3]1, 2), +(i48[3]1, 1))), ≥)∧0 = 0∧0 = 0∧[(3)bni_46 + (-1)Bound*bni_46] + [bni_46]i48[2] + [bni_46]i51[2] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_47] ≥ 0)



    We simplified constraint (110) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (111)    ([3] ≥ 0∧i48[2] ≥ 0∧[1] ≥ 0∧i48[2] + [1] ≥ 0∧0 ≥ 0∧0 ≥ 0 ⇒ (UIncreasing(LOAD583(i36[3]1, i33[3]1, -(i51[3]1, 2), +(i48[3]1, 1))), ≥)∧0 = 0∧0 = 0∧[(3)bni_46 + (-1)Bound*bni_46] + [bni_46]i48[2] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_47] ≥ 0)



    We simplified constraint (111) using rule (IDP_POLY_GCD) which results in the following new constraint:

    (112)    (i48[2] ≥ 0∧[1] ≥ 0∧i48[2] + [1] ≥ 0∧0 ≥ 0∧0 ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[3]1, i33[3]1, -(i51[3]1, 2), +(i48[3]1, 1))), ≥)∧0 = 0∧0 = 0∧[(3)bni_46 + (-1)Bound*bni_46] + [bni_46]i48[2] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_47] ≥ 0)



  • We consider the chain LOAD583(i36[2], i33[2], i51[2], i48[2]) → COND_LOAD583(&&(>(i51[2], 1), >(+(i48[2], 1), 0)), i36[2], i33[2], i51[2], i48[2]), COND_LOAD583(TRUE, i36[3], i33[3], i51[3], i48[3]) → LOAD583(i36[3], i33[3], -(i51[3], 2), +(i48[3], 1)), LOAD583(i36[2], i33[2], i51[2], i48[2]) → COND_LOAD583(&&(>(i51[2], 1), >(+(i48[2], 1), 0)), i36[2], i33[2], i51[2], i48[2]), COND_LOAD583(TRUE, i36[3], i33[3], i51[3], i48[3]) → LOAD583(i36[3], i33[3], -(i51[3], 2), +(i48[3], 1)), LOAD583(i36[7], i33[7], i50[7], i48[7]) → COND_LOAD5832(&&(&&(<=(i50[7], 1), >(+(i33[7], 1), 0)), >(+(i48[7], 1), 0)), i36[7], i33[7], i50[7], i48[7]), COND_LOAD5832(TRUE, i36[8], i33[8], i50[8], i48[8]) → LOAD416(+(i48[8], 1), +(i33[8], 1)) which results in the following constraint:

    (113)    (i36[2]=i36[3]∧i51[2]=i51[3]∧i33[2]=i33[3]∧i48[2]=i48[3]∧&&(>(i51[2], 1), >(+(i48[2], 1), 0))=TRUE∧+(i48[3], 1)=i48[2]1∧-(i51[3], 2)=i51[2]1∧i33[3]=i33[2]1∧i36[3]=i36[2]1∧i36[2]1=i36[3]1∧i51[2]1=i51[3]1∧i33[2]1=i33[3]1∧i48[2]1=i48[3]1∧&&(>(i51[2]1, 1), >(+(i48[2]1, 1), 0))=TRUE∧+(i48[3]1, 1)=i48[7]∧-(i51[3]1, 2)=i50[7]∧i36[3]1=i36[7]∧i33[3]1=i33[7]∧i50[7]=i50[8]∧i33[7]=i33[8]∧i36[7]=i36[8]∧i48[7]=i48[8]∧&&(&&(<=(i50[7], 1), >(+(i33[7], 1), 0)), >(+(i48[7], 1), 0))=TRUE ⇒ COND_LOAD583(TRUE, i36[3]1, i33[3]1, i51[3]1, i48[3]1)≥NonInfC∧COND_LOAD583(TRUE, i36[3]1, i33[3]1, i51[3]1, i48[3]1)≥LOAD583(i36[3]1, i33[3]1, -(i51[3]1, 2), +(i48[3]1, 1))∧(UIncreasing(LOAD583(i36[3]1, i33[3]1, -(i51[3]1, 2), +(i48[3]1, 1))), ≥))



    We simplified constraint (113) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (114)    (>(i51[2], 1)=TRUE∧>(+(i48[2], 1), 0)=TRUE∧>(-(i51[2], 2), 1)=TRUE∧>(+(+(i48[2], 1), 1), 0)=TRUE∧>(+(+(+(i48[2], 1), 1), 1), 0)=TRUE∧<=(-(-(i51[2], 2), 2), 1)=TRUE∧>(+(i33[7], 1), 0)=TRUE ⇒ COND_LOAD583(TRUE, i36[2], i33[7], -(i51[2], 2), +(i48[2], 1))≥NonInfC∧COND_LOAD583(TRUE, i36[2], i33[7], -(i51[2], 2), +(i48[2], 1))≥LOAD583(i36[2], i33[7], -(-(i51[2], 2), 2), +(+(i48[2], 1), 1))∧(UIncreasing(LOAD583(i36[3]1, i33[3]1, -(i51[3]1, 2), +(i48[3]1, 1))), ≥))



    We simplified constraint (114) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (115)    (i51[2] + [-2] ≥ 0∧i48[2] ≥ 0∧i51[2] + [-4] ≥ 0∧i48[2] + [1] ≥ 0∧i48[2] + [2] ≥ 0∧[5] + [-1]i51[2] ≥ 0∧i33[7] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[3]1, i33[3]1, -(i51[3]1, 2), +(i48[3]1, 1))), ≥)∧[(-2)bni_46 + (-1)Bound*bni_46] + [bni_46]i48[2] + [bni_46]i51[2] ≥ 0∧[(-1)bso_47] ≥ 0)



    We simplified constraint (115) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (116)    (i51[2] + [-2] ≥ 0∧i48[2] ≥ 0∧i51[2] + [-4] ≥ 0∧i48[2] + [1] ≥ 0∧i48[2] + [2] ≥ 0∧[5] + [-1]i51[2] ≥ 0∧i33[7] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[3]1, i33[3]1, -(i51[3]1, 2), +(i48[3]1, 1))), ≥)∧[(-2)bni_46 + (-1)Bound*bni_46] + [bni_46]i48[2] + [bni_46]i51[2] ≥ 0∧[(-1)bso_47] ≥ 0)



    We simplified constraint (116) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (117)    (i51[2] + [-2] ≥ 0∧i48[2] ≥ 0∧i51[2] + [-4] ≥ 0∧i48[2] + [1] ≥ 0∧i48[2] + [2] ≥ 0∧[5] + [-1]i51[2] ≥ 0∧i33[7] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[3]1, i33[3]1, -(i51[3]1, 2), +(i48[3]1, 1))), ≥)∧[(-2)bni_46 + (-1)Bound*bni_46] + [bni_46]i48[2] + [bni_46]i51[2] ≥ 0∧[(-1)bso_47] ≥ 0)



    We simplified constraint (117) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

    (118)    (i51[2] + [-2] ≥ 0∧i48[2] ≥ 0∧i51[2] + [-4] ≥ 0∧i48[2] + [1] ≥ 0∧i48[2] + [2] ≥ 0∧[5] + [-1]i51[2] ≥ 0∧i33[7] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[3]1, i33[3]1, -(i51[3]1, 2), +(i48[3]1, 1))), ≥)∧0 = 0∧[(-2)bni_46 + (-1)Bound*bni_46] + [bni_46]i48[2] + [bni_46]i51[2] ≥ 0∧0 = 0∧[(-1)bso_47] ≥ 0)



    We simplified constraint (118) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (119)    (i51[2] ≥ 0∧i48[2] ≥ 0∧[-2] + i51[2] ≥ 0∧i48[2] + [1] ≥ 0∧i48[2] + [2] ≥ 0∧[3] + [-1]i51[2] ≥ 0∧i33[7] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[3]1, i33[3]1, -(i51[3]1, 2), +(i48[3]1, 1))), ≥)∧0 = 0∧[(-1)Bound*bni_46] + [bni_46]i48[2] + [bni_46]i51[2] ≥ 0∧0 = 0∧[(-1)bso_47] ≥ 0)



    We simplified constraint (119) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (120)    ([2] + i51[2] ≥ 0∧i48[2] ≥ 0∧i51[2] ≥ 0∧i48[2] + [1] ≥ 0∧i48[2] + [2] ≥ 0∧[1] + [-1]i51[2] ≥ 0∧i33[7] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[3]1, i33[3]1, -(i51[3]1, 2), +(i48[3]1, 1))), ≥)∧0 = 0∧[(2)bni_46 + (-1)Bound*bni_46] + [bni_46]i48[2] + [bni_46]i51[2] ≥ 0∧0 = 0∧[(-1)bso_47] ≥ 0)



    We simplified constraint (120) using rule (IDP_POLY_GCD) which results in the following new constraint:

    (121)    ([2] + i51[2] ≥ 0∧i48[2] ≥ 0∧i51[2] ≥ 0∧i48[2] + [1] ≥ 0∧[1] + [-1]i51[2] ≥ 0∧i33[7] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[3]1, i33[3]1, -(i51[3]1, 2), +(i48[3]1, 1))), ≥)∧0 = 0∧[(2)bni_46 + (-1)Bound*bni_46] + [bni_46]i48[2] + [bni_46]i51[2] ≥ 0∧0 = 0∧[(-1)bso_47] ≥ 0)







For Pair LOAD583(i36, i33, i51, i48) → COND_LOAD5831(&&(>(i51, 0), <=(i51, 1)), i36, i33, i51, i48) the following chains were created:
  • We consider the chain LOAD583(i36[4], i33[4], i51[4], i48[4]) → COND_LOAD5831(&&(>(i51[4], 0), <=(i51[4], 1)), i36[4], i33[4], i51[4], i48[4]), COND_LOAD5831(TRUE, i36[5], i33[5], i51[5], i48[5]) → LOAD594(i36[5], i33[5], i48[5]) which results in the following constraint:

    (122)    (&&(>(i51[4], 0), <=(i51[4], 1))=TRUE∧i36[4]=i36[5]∧i51[4]=i51[5]∧i48[4]=i48[5]∧i33[4]=i33[5] ⇒ LOAD583(i36[4], i33[4], i51[4], i48[4])≥NonInfC∧LOAD583(i36[4], i33[4], i51[4], i48[4])≥COND_LOAD5831(&&(>(i51[4], 0), <=(i51[4], 1)), i36[4], i33[4], i51[4], i48[4])∧(UIncreasing(COND_LOAD5831(&&(>(i51[4], 0), <=(i51[4], 1)), i36[4], i33[4], i51[4], i48[4])), ≥))



    We simplified constraint (122) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (123)    (>(i51[4], 0)=TRUE∧<=(i51[4], 1)=TRUE ⇒ LOAD583(i36[4], i33[4], i51[4], i48[4])≥NonInfC∧LOAD583(i36[4], i33[4], i51[4], i48[4])≥COND_LOAD5831(&&(>(i51[4], 0), <=(i51[4], 1)), i36[4], i33[4], i51[4], i48[4])∧(UIncreasing(COND_LOAD5831(&&(>(i51[4], 0), <=(i51[4], 1)), i36[4], i33[4], i51[4], i48[4])), ≥))



    We simplified constraint (123) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (124)    (i51[4] + [-1] ≥ 0∧[1] + [-1]i51[4] ≥ 0 ⇒ (UIncreasing(COND_LOAD5831(&&(>(i51[4], 0), <=(i51[4], 1)), i36[4], i33[4], i51[4], i48[4])), ≥)∧[(-1)Bound*bni_48] + [bni_48]i48[4] + [bni_48]i51[4] ≥ 0∧[-1 + (-1)bso_49] + i51[4] ≥ 0)



    We simplified constraint (124) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (125)    (i51[4] + [-1] ≥ 0∧[1] + [-1]i51[4] ≥ 0 ⇒ (UIncreasing(COND_LOAD5831(&&(>(i51[4], 0), <=(i51[4], 1)), i36[4], i33[4], i51[4], i48[4])), ≥)∧[(-1)Bound*bni_48] + [bni_48]i48[4] + [bni_48]i51[4] ≥ 0∧[-1 + (-1)bso_49] + i51[4] ≥ 0)



    We simplified constraint (125) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (126)    (i51[4] + [-1] ≥ 0∧[1] + [-1]i51[4] ≥ 0 ⇒ (UIncreasing(COND_LOAD5831(&&(>(i51[4], 0), <=(i51[4], 1)), i36[4], i33[4], i51[4], i48[4])), ≥)∧[(-1)Bound*bni_48] + [bni_48]i48[4] + [bni_48]i51[4] ≥ 0∧[-1 + (-1)bso_49] + i51[4] ≥ 0)



    We simplified constraint (126) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

    (127)    (i51[4] + [-1] ≥ 0∧[1] + [-1]i51[4] ≥ 0 ⇒ (UIncreasing(COND_LOAD5831(&&(>(i51[4], 0), <=(i51[4], 1)), i36[4], i33[4], i51[4], i48[4])), ≥)∧[bni_48] = 0∧0 = 0∧0 = 0∧[(-1)Bound*bni_48] + [bni_48]i51[4] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[-1 + (-1)bso_49] + i51[4] ≥ 0)



    We simplified constraint (127) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (128)    (i51[4] ≥ 0∧[-1]i51[4] ≥ 0 ⇒ (UIncreasing(COND_LOAD5831(&&(>(i51[4], 0), <=(i51[4], 1)), i36[4], i33[4], i51[4], i48[4])), ≥)∧[bni_48] = 0∧0 = 0∧0 = 0∧[(-1)Bound*bni_48 + bni_48] + [bni_48]i51[4] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_49] + i51[4] ≥ 0)



    We simplified constraint (128) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (129)    (0 ≥ 0∧0 ≥ 0 ⇒ (UIncreasing(COND_LOAD5831(&&(>(i51[4], 0), <=(i51[4], 1)), i36[4], i33[4], i51[4], i48[4])), ≥)∧[bni_48] = 0∧0 = 0∧0 = 0∧[(-1)Bound*bni_48 + bni_48] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_49] ≥ 0)







For Pair COND_LOAD5831(TRUE, i36, i33, i51, i48) → LOAD594(i36, i33, i48) the following chains were created:
  • We consider the chain COND_LOAD5831(TRUE, i36[5], i33[5], i51[5], i48[5]) → LOAD594(i36[5], i33[5], i48[5]), LOAD594(i36[6], i33[6], i48[6]) → LOAD416(+(i48[6], 1), +(i33[6], 1)) which results in the following constraint:

    (130)    (i48[5]=i48[6]∧i36[5]=i36[6]∧i33[5]=i33[6] ⇒ COND_LOAD5831(TRUE, i36[5], i33[5], i51[5], i48[5])≥NonInfC∧COND_LOAD5831(TRUE, i36[5], i33[5], i51[5], i48[5])≥LOAD594(i36[5], i33[5], i48[5])∧(UIncreasing(LOAD594(i36[5], i33[5], i48[5])), ≥))



    We simplified constraint (130) using rule (IV) which results in the following new constraint:

    (131)    (COND_LOAD5831(TRUE, i36[5], i33[5], i51[5], i48[5])≥NonInfC∧COND_LOAD5831(TRUE, i36[5], i33[5], i51[5], i48[5])≥LOAD594(i36[5], i33[5], i48[5])∧(UIncreasing(LOAD594(i36[5], i33[5], i48[5])), ≥))



    We simplified constraint (131) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (132)    ((UIncreasing(LOAD594(i36[5], i33[5], i48[5])), ≥)∧[(-1)bso_51] ≥ 0)



    We simplified constraint (132) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (133)    ((UIncreasing(LOAD594(i36[5], i33[5], i48[5])), ≥)∧[(-1)bso_51] ≥ 0)



    We simplified constraint (133) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (134)    ((UIncreasing(LOAD594(i36[5], i33[5], i48[5])), ≥)∧[(-1)bso_51] ≥ 0)



    We simplified constraint (134) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

    (135)    ((UIncreasing(LOAD594(i36[5], i33[5], i48[5])), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_51] ≥ 0)







For Pair LOAD594(i36, i33, i48) → LOAD416(+(i48, 1), +(i33, 1)) the following chains were created:
  • We consider the chain COND_LOAD416(TRUE, i36[1], i33[1]) → LOAD583(i36[1], i33[1], -(i36[1], 2), 0), LOAD583(i36[4], i33[4], i51[4], i48[4]) → COND_LOAD5831(&&(>(i51[4], 0), <=(i51[4], 1)), i36[4], i33[4], i51[4], i48[4]), COND_LOAD5831(TRUE, i36[5], i33[5], i51[5], i48[5]) → LOAD594(i36[5], i33[5], i48[5]), LOAD594(i36[6], i33[6], i48[6]) → LOAD416(+(i48[6], 1), +(i33[6], 1)), LOAD416(i36[0], i33[0]) → COND_LOAD416(>(i36[0], 1), i36[0], i33[0]), COND_LOAD416(TRUE, i36[1], i33[1]) → LOAD583(i36[1], i33[1], -(i36[1], 2), 0) which results in the following constraint:

    (136)    (i33[1]=i33[4]∧i36[1]=i36[4]∧0=i48[4]∧-(i36[1], 2)=i51[4]∧&&(>(i51[4], 0), <=(i51[4], 1))=TRUE∧i36[4]=i36[5]∧i51[4]=i51[5]∧i48[4]=i48[5]∧i33[4]=i33[5]∧i48[5]=i48[6]∧i36[5]=i36[6]∧i33[5]=i33[6]∧+(i33[6], 1)=i33[0]∧+(i48[6], 1)=i36[0]∧i33[0]=i33[1]1∧>(i36[0], 1)=TRUE∧i36[0]=i36[1]1 ⇒ LOAD594(i36[6], i33[6], i48[6])≥NonInfC∧LOAD594(i36[6], i33[6], i48[6])≥LOAD416(+(i48[6], 1), +(i33[6], 1))∧(UIncreasing(LOAD416(+(i48[6], 1), +(i33[6], 1))), ≥))



    We solved constraint (136) using rules (I), (II), (III), (IV), (IDP_CONSTANT_FOLD), (IDP_BOOLEAN).
  • We consider the chain COND_LOAD583(TRUE, i36[3], i33[3], i51[3], i48[3]) → LOAD583(i36[3], i33[3], -(i51[3], 2), +(i48[3], 1)), LOAD583(i36[4], i33[4], i51[4], i48[4]) → COND_LOAD5831(&&(>(i51[4], 0), <=(i51[4], 1)), i36[4], i33[4], i51[4], i48[4]), COND_LOAD5831(TRUE, i36[5], i33[5], i51[5], i48[5]) → LOAD594(i36[5], i33[5], i48[5]), LOAD594(i36[6], i33[6], i48[6]) → LOAD416(+(i48[6], 1), +(i33[6], 1)), LOAD416(i36[0], i33[0]) → COND_LOAD416(>(i36[0], 1), i36[0], i33[0]), COND_LOAD416(TRUE, i36[1], i33[1]) → LOAD583(i36[1], i33[1], -(i36[1], 2), 0) which results in the following constraint:

    (137)    (+(i48[3], 1)=i48[4]∧i36[3]=i36[4]∧i33[3]=i33[4]∧-(i51[3], 2)=i51[4]∧&&(>(i51[4], 0), <=(i51[4], 1))=TRUE∧i36[4]=i36[5]∧i51[4]=i51[5]∧i48[4]=i48[5]∧i33[4]=i33[5]∧i48[5]=i48[6]∧i36[5]=i36[6]∧i33[5]=i33[6]∧+(i33[6], 1)=i33[0]∧+(i48[6], 1)=i36[0]∧i33[0]=i33[1]∧>(i36[0], 1)=TRUE∧i36[0]=i36[1] ⇒ LOAD594(i36[6], i33[6], i48[6])≥NonInfC∧LOAD594(i36[6], i33[6], i48[6])≥LOAD416(+(i48[6], 1), +(i33[6], 1))∧(UIncreasing(LOAD416(+(i48[6], 1), +(i33[6], 1))), ≥))



    We simplified constraint (137) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (138)    (>(+(+(i48[3], 1), 1), 1)=TRUE∧>(-(i51[3], 2), 0)=TRUE∧<=(-(i51[3], 2), 1)=TRUE ⇒ LOAD594(i36[3], i33[3], +(i48[3], 1))≥NonInfC∧LOAD594(i36[3], i33[3], +(i48[3], 1))≥LOAD416(+(+(i48[3], 1), 1), +(i33[3], 1))∧(UIncreasing(LOAD416(+(i48[6], 1), +(i33[6], 1))), ≥))



    We simplified constraint (138) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (139)    (i48[3] ≥ 0∧i51[3] + [-3] ≥ 0∧[3] + [-1]i51[3] ≥ 0 ⇒ (UIncreasing(LOAD416(+(i48[6], 1), +(i33[6], 1))), ≥)∧[bni_52 + (-1)Bound*bni_52] + [bni_52]i48[3] ≥ 0∧[(-1)bso_53] ≥ 0)



    We simplified constraint (139) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (140)    (i48[3] ≥ 0∧i51[3] + [-3] ≥ 0∧[3] + [-1]i51[3] ≥ 0 ⇒ (UIncreasing(LOAD416(+(i48[6], 1), +(i33[6], 1))), ≥)∧[bni_52 + (-1)Bound*bni_52] + [bni_52]i48[3] ≥ 0∧[(-1)bso_53] ≥ 0)



    We simplified constraint (140) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (141)    (i48[3] ≥ 0∧i51[3] + [-3] ≥ 0∧[3] + [-1]i51[3] ≥ 0 ⇒ (UIncreasing(LOAD416(+(i48[6], 1), +(i33[6], 1))), ≥)∧[bni_52 + (-1)Bound*bni_52] + [bni_52]i48[3] ≥ 0∧[(-1)bso_53] ≥ 0)



    We simplified constraint (141) using rules (IDP_UNRESTRICTED_VARS), (IDP_POLY_GCD) which results in the following new constraint:

    (142)    (i48[3] ≥ 0∧[3] + [-1]i51[3] ≥ 0∧[-1] ≥ 0 ⇒ (UIncreasing(LOAD416(+(i48[6], 1), +(i33[6], 1))), ≥)∧0 = 0∧0 = 0∧[bni_52 + (-1)Bound*bni_52] + [bni_52]i48[3] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_53] ≥ 0)







For Pair LOAD583(i36, i33, i50, i48) → COND_LOAD5832(&&(&&(<=(i50, 1), >(+(i33, 1), 0)), >(+(i48, 1), 0)), i36, i33, i50, i48) the following chains were created:
  • We consider the chain LOAD583(i36[7], i33[7], i50[7], i48[7]) → COND_LOAD5832(&&(&&(<=(i50[7], 1), >(+(i33[7], 1), 0)), >(+(i48[7], 1), 0)), i36[7], i33[7], i50[7], i48[7]), COND_LOAD5832(TRUE, i36[8], i33[8], i50[8], i48[8]) → LOAD416(+(i48[8], 1), +(i33[8], 1)) which results in the following constraint:

    (143)    (i50[7]=i50[8]∧i33[7]=i33[8]∧i36[7]=i36[8]∧i48[7]=i48[8]∧&&(&&(<=(i50[7], 1), >(+(i33[7], 1), 0)), >(+(i48[7], 1), 0))=TRUE ⇒ LOAD583(i36[7], i33[7], i50[7], i48[7])≥NonInfC∧LOAD583(i36[7], i33[7], i50[7], i48[7])≥COND_LOAD5832(&&(&&(<=(i50[7], 1), >(+(i33[7], 1), 0)), >(+(i48[7], 1), 0)), i36[7], i33[7], i50[7], i48[7])∧(UIncreasing(COND_LOAD5832(&&(&&(<=(i50[7], 1), >(+(i33[7], 1), 0)), >(+(i48[7], 1), 0)), i36[7], i33[7], i50[7], i48[7])), ≥))



    We simplified constraint (143) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (144)    (>(+(i48[7], 1), 0)=TRUE∧<=(i50[7], 1)=TRUE∧>(+(i33[7], 1), 0)=TRUE ⇒ LOAD583(i36[7], i33[7], i50[7], i48[7])≥NonInfC∧LOAD583(i36[7], i33[7], i50[7], i48[7])≥COND_LOAD5832(&&(&&(<=(i50[7], 1), >(+(i33[7], 1), 0)), >(+(i48[7], 1), 0)), i36[7], i33[7], i50[7], i48[7])∧(UIncreasing(COND_LOAD5832(&&(&&(<=(i50[7], 1), >(+(i33[7], 1), 0)), >(+(i48[7], 1), 0)), i36[7], i33[7], i50[7], i48[7])), ≥))



    We simplified constraint (144) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (145)    (i48[7] ≥ 0∧[1] + [-1]i50[7] ≥ 0∧i33[7] ≥ 0 ⇒ (UIncreasing(COND_LOAD5832(&&(&&(<=(i50[7], 1), >(+(i33[7], 1), 0)), >(+(i48[7], 1), 0)), i36[7], i33[7], i50[7], i48[7])), ≥)∧[(-1)Bound*bni_54] + [bni_54]i48[7] + [bni_54]i50[7] ≥ 0∧[(-1)bso_55] ≥ 0)



    We simplified constraint (145) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (146)    (i48[7] ≥ 0∧[1] + [-1]i50[7] ≥ 0∧i33[7] ≥ 0 ⇒ (UIncreasing(COND_LOAD5832(&&(&&(<=(i50[7], 1), >(+(i33[7], 1), 0)), >(+(i48[7], 1), 0)), i36[7], i33[7], i50[7], i48[7])), ≥)∧[(-1)Bound*bni_54] + [bni_54]i48[7] + [bni_54]i50[7] ≥ 0∧[(-1)bso_55] ≥ 0)



    We simplified constraint (146) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (147)    (i48[7] ≥ 0∧[1] + [-1]i50[7] ≥ 0∧i33[7] ≥ 0 ⇒ (UIncreasing(COND_LOAD5832(&&(&&(<=(i50[7], 1), >(+(i33[7], 1), 0)), >(+(i48[7], 1), 0)), i36[7], i33[7], i50[7], i48[7])), ≥)∧[(-1)Bound*bni_54] + [bni_54]i48[7] + [bni_54]i50[7] ≥ 0∧[(-1)bso_55] ≥ 0)



    We simplified constraint (147) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

    (148)    (i48[7] ≥ 0∧[1] + [-1]i50[7] ≥ 0∧i33[7] ≥ 0 ⇒ (UIncreasing(COND_LOAD5832(&&(&&(<=(i50[7], 1), >(+(i33[7], 1), 0)), >(+(i48[7], 1), 0)), i36[7], i33[7], i50[7], i48[7])), ≥)∧0 = 0∧[(-1)Bound*bni_54] + [bni_54]i48[7] + [bni_54]i50[7] ≥ 0∧0 = 0∧[(-1)bso_55] ≥ 0)



    We simplified constraint (148) using rule (IDP_SMT_SPLIT) which results in the following new constraints:

    (149)    (i48[7] ≥ 0∧[1] + [-1]i50[7] ≥ 0∧i33[7] ≥ 0∧i50[7] ≥ 0 ⇒ (UIncreasing(COND_LOAD5832(&&(&&(<=(i50[7], 1), >(+(i33[7], 1), 0)), >(+(i48[7], 1), 0)), i36[7], i33[7], i50[7], i48[7])), ≥)∧0 = 0∧[(-1)Bound*bni_54] + [bni_54]i48[7] + [bni_54]i50[7] ≥ 0∧0 = 0∧[(-1)bso_55] ≥ 0)


    (150)    (i48[7] ≥ 0∧[1] + i50[7] ≥ 0∧i33[7] ≥ 0∧i50[7] ≥ 0 ⇒ (UIncreasing(COND_LOAD5832(&&(&&(<=(i50[7], 1), >(+(i33[7], 1), 0)), >(+(i48[7], 1), 0)), i36[7], i33[7], i50[7], i48[7])), ≥)∧0 = 0∧[(-1)Bound*bni_54] + [bni_54]i48[7] + [(-1)bni_54]i50[7] ≥ 0∧0 = 0∧[(-1)bso_55] ≥ 0)







For Pair COND_LOAD5832(TRUE, i36, i33, i50, i48) → LOAD416(+(i48, 1), +(i33, 1)) the following chains were created:
  • We consider the chain LOAD416(i36[0], i33[0]) → COND_LOAD416(>(i36[0], 1), i36[0], i33[0]), COND_LOAD416(TRUE, i36[1], i33[1]) → LOAD583(i36[1], i33[1], -(i36[1], 2), 0), LOAD583(i36[7], i33[7], i50[7], i48[7]) → COND_LOAD5832(&&(&&(<=(i50[7], 1), >(+(i33[7], 1), 0)), >(+(i48[7], 1), 0)), i36[7], i33[7], i50[7], i48[7]), COND_LOAD5832(TRUE, i36[8], i33[8], i50[8], i48[8]) → LOAD416(+(i48[8], 1), +(i33[8], 1)), LOAD416(i36[0], i33[0]) → COND_LOAD416(>(i36[0], 1), i36[0], i33[0]), COND_LOAD416(TRUE, i36[1], i33[1]) → LOAD583(i36[1], i33[1], -(i36[1], 2), 0) which results in the following constraint:

    (151)    (i33[0]=i33[1]∧>(i36[0], 1)=TRUE∧i36[0]=i36[1]∧-(i36[1], 2)=i50[7]∧i33[1]=i33[7]∧0=i48[7]∧i36[1]=i36[7]∧i50[7]=i50[8]∧i33[7]=i33[8]∧i36[7]=i36[8]∧i48[7]=i48[8]∧&&(&&(<=(i50[7], 1), >(+(i33[7], 1), 0)), >(+(i48[7], 1), 0))=TRUE∧+(i48[8], 1)=i36[0]1∧+(i33[8], 1)=i33[0]1∧i33[0]1=i33[1]1∧>(i36[0]1, 1)=TRUE∧i36[0]1=i36[1]1 ⇒ COND_LOAD5832(TRUE, i36[8], i33[8], i50[8], i48[8])≥NonInfC∧COND_LOAD5832(TRUE, i36[8], i33[8], i50[8], i48[8])≥LOAD416(+(i48[8], 1), +(i33[8], 1))∧(UIncreasing(LOAD416(+(i48[8], 1), +(i33[8], 1))), ≥))



    We solved constraint (151) using rules (I), (II), (III), (IV), (IDP_CONSTANT_FOLD), (DELETE_TRIVIAL_REDUCESTO), (IDP_BOOLEAN).
  • We consider the chain LOAD583(i36[2], i33[2], i51[2], i48[2]) → COND_LOAD583(&&(>(i51[2], 1), >(+(i48[2], 1), 0)), i36[2], i33[2], i51[2], i48[2]), COND_LOAD583(TRUE, i36[3], i33[3], i51[3], i48[3]) → LOAD583(i36[3], i33[3], -(i51[3], 2), +(i48[3], 1)), LOAD583(i36[7], i33[7], i50[7], i48[7]) → COND_LOAD5832(&&(&&(<=(i50[7], 1), >(+(i33[7], 1), 0)), >(+(i48[7], 1), 0)), i36[7], i33[7], i50[7], i48[7]), COND_LOAD5832(TRUE, i36[8], i33[8], i50[8], i48[8]) → LOAD416(+(i48[8], 1), +(i33[8], 1)), LOAD416(i36[0], i33[0]) → COND_LOAD416(>(i36[0], 1), i36[0], i33[0]), COND_LOAD416(TRUE, i36[1], i33[1]) → LOAD583(i36[1], i33[1], -(i36[1], 2), 0) which results in the following constraint:

    (152)    (i36[2]=i36[3]∧i51[2]=i51[3]∧i33[2]=i33[3]∧i48[2]=i48[3]∧&&(>(i51[2], 1), >(+(i48[2], 1), 0))=TRUE∧+(i48[3], 1)=i48[7]∧-(i51[3], 2)=i50[7]∧i36[3]=i36[7]∧i33[3]=i33[7]∧i50[7]=i50[8]∧i33[7]=i33[8]∧i36[7]=i36[8]∧i48[7]=i48[8]∧&&(&&(<=(i50[7], 1), >(+(i33[7], 1), 0)), >(+(i48[7], 1), 0))=TRUE∧+(i48[8], 1)=i36[0]∧+(i33[8], 1)=i33[0]∧i33[0]=i33[1]∧>(i36[0], 1)=TRUE∧i36[0]=i36[1] ⇒ COND_LOAD5832(TRUE, i36[8], i33[8], i50[8], i48[8])≥NonInfC∧COND_LOAD5832(TRUE, i36[8], i33[8], i50[8], i48[8])≥LOAD416(+(i48[8], 1), +(i33[8], 1))∧(UIncreasing(LOAD416(+(i48[8], 1), +(i33[8], 1))), ≥))



    We simplified constraint (152) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (153)    (>(+(+(i48[2], 1), 1), 1)=TRUE∧>(i51[2], 1)=TRUE∧>(+(i48[2], 1), 0)=TRUE∧>(+(+(i48[2], 1), 1), 0)=TRUE∧<=(-(i51[2], 2), 1)=TRUE∧>(+(i33[7], 1), 0)=TRUE ⇒ COND_LOAD5832(TRUE, i36[2], i33[7], -(i51[2], 2), +(i48[2], 1))≥NonInfC∧COND_LOAD5832(TRUE, i36[2], i33[7], -(i51[2], 2), +(i48[2], 1))≥LOAD416(+(+(i48[2], 1), 1), +(i33[7], 1))∧(UIncreasing(LOAD416(+(i48[8], 1), +(i33[8], 1))), ≥))



    We simplified constraint (153) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (154)    (i48[2] ≥ 0∧i51[2] + [-2] ≥ 0∧i48[2] ≥ 0∧i48[2] + [1] ≥ 0∧[3] + [-1]i51[2] ≥ 0∧i33[7] ≥ 0 ⇒ (UIncreasing(LOAD416(+(i48[8], 1), +(i33[8], 1))), ≥)∧[(-1)bni_56 + (-1)Bound*bni_56] + [bni_56]i48[2] + [bni_56]i51[2] ≥ 0∧[-2 + (-1)bso_57] + i51[2] ≥ 0)



    We simplified constraint (154) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (155)    (i48[2] ≥ 0∧i51[2] + [-2] ≥ 0∧i48[2] ≥ 0∧i48[2] + [1] ≥ 0∧[3] + [-1]i51[2] ≥ 0∧i33[7] ≥ 0 ⇒ (UIncreasing(LOAD416(+(i48[8], 1), +(i33[8], 1))), ≥)∧[(-1)bni_56 + (-1)Bound*bni_56] + [bni_56]i48[2] + [bni_56]i51[2] ≥ 0∧[-2 + (-1)bso_57] + i51[2] ≥ 0)



    We simplified constraint (155) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (156)    (i48[2] ≥ 0∧i51[2] + [-2] ≥ 0∧i48[2] ≥ 0∧i48[2] + [1] ≥ 0∧[3] + [-1]i51[2] ≥ 0∧i33[7] ≥ 0 ⇒ (UIncreasing(LOAD416(+(i48[8], 1), +(i33[8], 1))), ≥)∧[(-1)bni_56 + (-1)Bound*bni_56] + [bni_56]i48[2] + [bni_56]i51[2] ≥ 0∧[-2 + (-1)bso_57] + i51[2] ≥ 0)



    We simplified constraint (156) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

    (157)    (i48[2] ≥ 0∧i51[2] + [-2] ≥ 0∧i48[2] ≥ 0∧i48[2] + [1] ≥ 0∧[3] + [-1]i51[2] ≥ 0∧i33[7] ≥ 0 ⇒ (UIncreasing(LOAD416(+(i48[8], 1), +(i33[8], 1))), ≥)∧0 = 0∧[(-1)bni_56 + (-1)Bound*bni_56] + [bni_56]i48[2] + [bni_56]i51[2] ≥ 0∧0 = 0∧[-2 + (-1)bso_57] + i51[2] ≥ 0)



    We simplified constraint (157) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (158)    (i48[2] ≥ 0∧i51[2] ≥ 0∧i48[2] ≥ 0∧i48[2] + [1] ≥ 0∧[1] + [-1]i51[2] ≥ 0∧i33[7] ≥ 0 ⇒ (UIncreasing(LOAD416(+(i48[8], 1), +(i33[8], 1))), ≥)∧0 = 0∧[bni_56 + (-1)Bound*bni_56] + [bni_56]i48[2] + [bni_56]i51[2] ≥ 0∧0 = 0∧[(-1)bso_57] + i51[2] ≥ 0)







To summarize, we get the following constraints P≥ for the following pairs.
  • LOAD416(i36, i33) → COND_LOAD416(>(i36, 1), i36, i33)
    • (i36[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD416(>(i36[0], 1), i36[0], i33[0])), ≥)∧0 = 0∧[bni_40 + (-1)Bound*bni_40] + [bni_40]i36[0] ≥ 0∧0 = 0∧[(-1)bso_41] ≥ 0)

  • COND_LOAD416(TRUE, i36, i33) → LOAD583(i36, i33, -(i36, 2), 0)
    • ([2] + i48[6] ≥ 0∧i48[6] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[1], i33[1], -(i36[1], 2), 0)), ≥)∧0 = 0∧[(-1)Bound*bni_42 + (3)bni_42] + [bni_42]i48[6] ≥ 0∧0 = 0∧[1 + (-1)bso_43] ≥ 0)
    • ([1] ≥ 0∧0 ≥ 0∧0 ≥ 0 ⇒ (UIncreasing(LOAD583(i36[1], i33[1], -(i36[1], 2), 0)), ≥)∧0 = 0∧[(-1)Bound*bni_42 + (2)bni_42] ≥ 0∧0 = 0∧[1 + (-1)bso_43] ≥ 0)
    • (i48[6] ≥ 0∧[1] + [-1]i48[6] ≥ 0∧i33[6] + [1] ≥ 0∧i33[6] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[1], i33[1], -(i36[1], 2), 0)), ≥)∧[(-1)Bound*bni_42 + bni_42] + [bni_42]i48[6] ≥ 0∧[1 + (-1)bso_43] ≥ 0)
    • (i48[6] ≥ 0∧[1] + [-1]i48[6] ≥ 0∧[-1]i33[6] + [1] ≥ 0∧i33[6] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[1], i33[1], -(i36[1], 2), 0)), ≥)∧[(-1)Bound*bni_42 + bni_42] + [bni_42]i48[6] ≥ 0∧[1 + (-1)bso_43] ≥ 0)
    • ([2] + i48[7] ≥ 0∧[3] + i48[7] ≥ 0∧i48[7] ≥ 0∧i33[7] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[1], i33[1], -(i36[1], 2), 0)), ≥)∧[(-1)Bound*bni_42 + (3)bni_42] + [bni_42]i48[7] ≥ 0∧[1 + (-1)bso_43] ≥ 0)
    • ([1] ≥ 0∧0 ≥ 0∧0 ≥ 0∧i33[7] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[1], i33[1], -(i36[1], 2), 0)), ≥)∧[(-1)Bound*bni_42 + (2)bni_42] ≥ 0∧[1 + (-1)bso_43] ≥ 0)
    • (i48[7] ≥ 0∧[1] + i48[7] ≥ 0∧i33[7] ≥ 0∧[1] + [-1]i48[7] ≥ 0∧i33[7] + [1] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[1], i33[1], -(i36[1], 2), 0)), ≥)∧[(-1)Bound*bni_42 + bni_42] + [bni_42]i48[7] ≥ 0∧[1 + (-1)bso_43] ≥ 0)

  • LOAD583(i36, i33, i51, i48) → COND_LOAD583(&&(>(i51, 1), >(+(i48, 1), 0)), i36, i33, i51, i48)
    • (i51[2] ≥ 0∧i48[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD583(&&(>(i51[2], 1), >(+(i48[2], 1), 0)), i36[2], i33[2], i51[2], i48[2])), ≥)∧0 = 0∧0 = 0∧[(-1)Bound*bni_44 + (2)bni_44] + [bni_44]i48[2] + [bni_44]i51[2] ≥ 0∧0 = 0∧0 = 0∧[1 + (-1)bso_45] ≥ 0)

  • COND_LOAD583(TRUE, i36, i33, i51, i48) → LOAD583(i36, i33, -(i51, 2), +(i48, 1))
    • ([4] + i36[0] ≥ 0∧[2] + i36[0] ≥ 0∧i36[0] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[3], i33[3], -(i51[3], 2), +(i48[3], 1))), ≥)∧0 = 0∧[(3)bni_46 + (-1)Bound*bni_46] + [bni_46]i36[0] ≥ 0∧0 = 0∧[(-1)bso_47] ≥ 0)
    • ([1] ≥ 0∧0 ≥ 0∧0 ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[3], i33[3], -(i51[3], 2), +(i48[3], 1))), ≥)∧0 = 0∧[(2)bni_46 + (-1)Bound*bni_46] ≥ 0∧0 = 0∧[(-1)bso_47] ≥ 0)
    • ([2] + i36[0] ≥ 0∧i36[0] ≥ 0∧[1] + [-1]i36[0] ≥ 0∧i33[7] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[3], i33[3], -(i51[3], 2), +(i48[3], 1))), ≥)∧[bni_46 + (-1)Bound*bni_46] + [bni_46]i36[0] ≥ 0∧[(-1)bso_47] ≥ 0)
    • ([4] + i51[2] ≥ 0∧i48[2] ≥ 0∧[2] + i51[2] ≥ 0∧i48[2] + [1] ≥ 0∧i51[2] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[3]1, i33[3]1, -(i51[3]1, 2), +(i48[3]1, 1))), ≥)∧0 = 0∧0 = 0∧[(4)bni_46 + (-1)Bound*bni_46] + [bni_46]i48[2] + [bni_46]i51[2] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_47] ≥ 0)
    • (i48[2] ≥ 0∧[1] ≥ 0∧i48[2] + [1] ≥ 0∧0 ≥ 0∧0 ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[3]1, i33[3]1, -(i51[3]1, 2), +(i48[3]1, 1))), ≥)∧0 = 0∧0 = 0∧[(3)bni_46 + (-1)Bound*bni_46] + [bni_46]i48[2] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_47] ≥ 0)
    • ([2] + i51[2] ≥ 0∧i48[2] ≥ 0∧i51[2] ≥ 0∧i48[2] + [1] ≥ 0∧[1] + [-1]i51[2] ≥ 0∧i33[7] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(LOAD583(i36[3]1, i33[3]1, -(i51[3]1, 2), +(i48[3]1, 1))), ≥)∧0 = 0∧[(2)bni_46 + (-1)Bound*bni_46] + [bni_46]i48[2] + [bni_46]i51[2] ≥ 0∧0 = 0∧[(-1)bso_47] ≥ 0)

  • LOAD583(i36, i33, i51, i48) → COND_LOAD5831(&&(>(i51, 0), <=(i51, 1)), i36, i33, i51, i48)
    • (0 ≥ 0∧0 ≥ 0 ⇒ (UIncreasing(COND_LOAD5831(&&(>(i51[4], 0), <=(i51[4], 1)), i36[4], i33[4], i51[4], i48[4])), ≥)∧[bni_48] = 0∧0 = 0∧0 = 0∧[(-1)Bound*bni_48 + bni_48] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_49] ≥ 0)

  • COND_LOAD5831(TRUE, i36, i33, i51, i48) → LOAD594(i36, i33, i48)
    • ((UIncreasing(LOAD594(i36[5], i33[5], i48[5])), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_51] ≥ 0)

  • LOAD594(i36, i33, i48) → LOAD416(+(i48, 1), +(i33, 1))
    • (i48[3] ≥ 0∧[3] + [-1]i51[3] ≥ 0∧[-1] ≥ 0 ⇒ (UIncreasing(LOAD416(+(i48[6], 1), +(i33[6], 1))), ≥)∧0 = 0∧0 = 0∧[bni_52 + (-1)Bound*bni_52] + [bni_52]i48[3] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_53] ≥ 0)

  • LOAD583(i36, i33, i50, i48) → COND_LOAD5832(&&(&&(<=(i50, 1), >(+(i33, 1), 0)), >(+(i48, 1), 0)), i36, i33, i50, i48)
    • (i48[7] ≥ 0∧[1] + [-1]i50[7] ≥ 0∧i33[7] ≥ 0∧i50[7] ≥ 0 ⇒ (UIncreasing(COND_LOAD5832(&&(&&(<=(i50[7], 1), >(+(i33[7], 1), 0)), >(+(i48[7], 1), 0)), i36[7], i33[7], i50[7], i48[7])), ≥)∧0 = 0∧[(-1)Bound*bni_54] + [bni_54]i48[7] + [bni_54]i50[7] ≥ 0∧0 = 0∧[(-1)bso_55] ≥ 0)
    • (i48[7] ≥ 0∧[1] + i50[7] ≥ 0∧i33[7] ≥ 0∧i50[7] ≥ 0 ⇒ (UIncreasing(COND_LOAD5832(&&(&&(<=(i50[7], 1), >(+(i33[7], 1), 0)), >(+(i48[7], 1), 0)), i36[7], i33[7], i50[7], i48[7])), ≥)∧0 = 0∧[(-1)Bound*bni_54] + [bni_54]i48[7] + [(-1)bni_54]i50[7] ≥ 0∧0 = 0∧[(-1)bso_55] ≥ 0)

  • COND_LOAD5832(TRUE, i36, i33, i50, i48) → LOAD416(+(i48, 1), +(i33, 1))
    • (i48[2] ≥ 0∧i51[2] ≥ 0∧i48[2] ≥ 0∧i48[2] + [1] ≥ 0∧[1] + [-1]i51[2] ≥ 0∧i33[7] ≥ 0 ⇒ (UIncreasing(LOAD416(+(i48[8], 1), +(i33[8], 1))), ≥)∧0 = 0∧[bni_56 + (-1)Bound*bni_56] + [bni_56]i48[2] + [bni_56]i51[2] ≥ 0∧0 = 0∧[(-1)bso_57] + i51[2] ≥ 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(LOAD416(x1, x2)) = [-1] + x1   
POL(COND_LOAD416(x1, x2, x3)) = [-1] + x2   
POL(>(x1, x2)) = [-1]   
POL(1) = [1]   
POL(LOAD583(x1, x2, x3, x4)) = x4 + x3   
POL(-(x1, x2)) = x1 + [-1]x2   
POL(2) = [2]   
POL(0) = 0   
POL(COND_LOAD583(x1, x2, x3, x4, x5)) = [-1] + x5 + x4   
POL(&&(x1, x2)) = [-1]   
POL(+(x1, x2)) = x1 + x2   
POL(COND_LOAD5831(x1, x2, x3, x4, x5)) = x5 + [-1]x1   
POL(<=(x1, x2)) = [-1]   
POL(LOAD594(x1, x2, x3)) = x3   
POL(COND_LOAD5832(x1, x2, x3, x4, x5)) = x5 + x4   

The following pairs are in P>:

COND_LOAD416(TRUE, i36[1], i33[1]) → LOAD583(i36[1], i33[1], -(i36[1], 2), 0)
LOAD583(i36[2], i33[2], i51[2], i48[2]) → COND_LOAD583(&&(>(i51[2], 1), >(+(i48[2], 1), 0)), i36[2], i33[2], i51[2], i48[2])
LOAD594(i36[6], i33[6], i48[6]) → LOAD416(+(i48[6], 1), +(i33[6], 1))

The following pairs are in Pbound:

LOAD416(i36[0], i33[0]) → COND_LOAD416(>(i36[0], 1), i36[0], i33[0])
COND_LOAD416(TRUE, i36[1], i33[1]) → LOAD583(i36[1], i33[1], -(i36[1], 2), 0)
LOAD583(i36[2], i33[2], i51[2], i48[2]) → COND_LOAD583(&&(>(i51[2], 1), >(+(i48[2], 1), 0)), i36[2], i33[2], i51[2], i48[2])
COND_LOAD583(TRUE, i36[3], i33[3], i51[3], i48[3]) → LOAD583(i36[3], i33[3], -(i51[3], 2), +(i48[3], 1))
LOAD594(i36[6], i33[6], i48[6]) → LOAD416(+(i48[6], 1), +(i33[6], 1))
COND_LOAD5832(TRUE, i36[8], i33[8], i50[8], i48[8]) → LOAD416(+(i48[8], 1), +(i33[8], 1))

The following pairs are in P≥:

LOAD416(i36[0], i33[0]) → COND_LOAD416(>(i36[0], 1), i36[0], i33[0])
COND_LOAD583(TRUE, i36[3], i33[3], i51[3], i48[3]) → LOAD583(i36[3], i33[3], -(i51[3], 2), +(i48[3], 1))
LOAD583(i36[4], i33[4], i51[4], i48[4]) → COND_LOAD5831(&&(>(i51[4], 0), <=(i51[4], 1)), i36[4], i33[4], i51[4], i48[4])
COND_LOAD5831(TRUE, i36[5], i33[5], i51[5], i48[5]) → LOAD594(i36[5], i33[5], i48[5])
LOAD583(i36[7], i33[7], i50[7], i48[7]) → COND_LOAD5832(&&(&&(<=(i50[7], 1), >(+(i33[7], 1), 0)), >(+(i48[7], 1), 0)), i36[7], i33[7], i50[7], i48[7])
COND_LOAD5832(TRUE, i36[8], i33[8], i50[8], i48[8]) → LOAD416(+(i48[8], 1), +(i33[8], 1))

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

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

(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:

Integer, Boolean


R is empty.

The integer pair graph contains the following rules and edges:
(0): LOAD416(i36[0], i33[0]) → COND_LOAD416(i36[0] > 1, i36[0], i33[0])
(3): COND_LOAD583(TRUE, i36[3], i33[3], i51[3], i48[3]) → LOAD583(i36[3], i33[3], i51[3] - 2, i48[3] + 1)
(4): LOAD583(i36[4], i33[4], i51[4], i48[4]) → COND_LOAD5831(i51[4] > 0 && i51[4] <= 1, i36[4], i33[4], i51[4], i48[4])
(5): COND_LOAD5831(TRUE, i36[5], i33[5], i51[5], i48[5]) → LOAD594(i36[5], i33[5], i48[5])
(7): LOAD583(i36[7], i33[7], i50[7], i48[7]) → COND_LOAD5832(i50[7] <= 1 && i33[7] + 1 > 0 && i48[7] + 1 > 0, i36[7], i33[7], i50[7], i48[7])
(8): COND_LOAD5832(TRUE, i36[8], i33[8], i50[8], i48[8]) → LOAD416(i48[8] + 1, i33[8] + 1)

(8) -> (0), if ((i48[8] + 1 →* i36[0])∧(i33[8] + 1 →* i33[0]))


(3) -> (4), if ((i48[3] + 1 →* i48[4])∧(i36[3] →* i36[4])∧(i33[3] →* i33[4])∧(i51[3] - 2 →* i51[4]))


(4) -> (5), if ((i51[4] > 0 && i51[4] <= 1 →* TRUE)∧(i36[4] →* i36[5])∧(i51[4] →* i51[5])∧(i48[4] →* i48[5])∧(i33[4] →* i33[5]))


(3) -> (7), if ((i48[3] + 1 →* i48[7])∧(i51[3] - 2 →* i50[7])∧(i36[3] →* i36[7])∧(i33[3] →* i33[7]))


(7) -> (8), if ((i50[7] →* i50[8])∧(i33[7] →* i33[8])∧(i36[7] →* i36[8])∧(i48[7] →* i48[8])∧(i50[7] <= 1 && i33[7] + 1 > 0 && i48[7] + 1 > 0 →* TRUE))



The set Q consists of the following terms:
Load416(x0, x1)
Cond_Load416(TRUE, x0, x1)
Load583(x0, x1, x2, x3)
Cond_Load583(TRUE, x0, x1, x2, x3)
Cond_Load5831(TRUE, x0, x1, x2, x3)
Load594(x0, x1, x2)
Cond_Load5832(TRUE, x0, x1, x2, x3)

(14) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 6 less nodes.

(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:

Boolean, Integer


R is empty.

The integer pair graph contains the following rules and edges:
(4): LOAD583(i36[4], i33[4], i51[4], i48[4]) → COND_LOAD5831(i51[4] > 0 && i51[4] <= 1, i36[4], i33[4], i51[4], i48[4])
(5): COND_LOAD5831(TRUE, i36[5], i33[5], i51[5], i48[5]) → LOAD594(i36[5], i33[5], i48[5])
(7): LOAD583(i36[7], i33[7], i50[7], i48[7]) → COND_LOAD5832(i50[7] <= 1 && i33[7] + 1 > 0 && i48[7] + 1 > 0, i36[7], i33[7], i50[7], i48[7])

(4) -> (5), if ((i51[4] > 0 && i51[4] <= 1 →* TRUE)∧(i36[4] →* i36[5])∧(i51[4] →* i51[5])∧(i48[4] →* i48[5])∧(i33[4] →* i33[5]))



The set Q consists of the following terms:
Load416(x0, x1)
Cond_Load416(TRUE, x0, x1)
Load583(x0, x1, x2, x3)
Cond_Load583(TRUE, x0, x1, x2, x3)
Cond_Load5831(TRUE, x0, x1, x2, x3)
Load594(x0, x1, x2)
Cond_Load5832(TRUE, x0, x1, x2, x3)

(17) IDependencyGraphProof (EQUIVALENT transformation)

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

(18) TRUE