Termination of the given JBC could be proven:

0 JBC
↳1 JBC2FIG (⇐)
↳2 FIGraph
↳3 FIGtoITRSProof (⇐)
↳4 ITRS
↳5 ITRStoIDPProof (⇔)
↳6 IDP
↳7 UsableRulesProof (⇔)
↳8 IDP
↳9 IDPNonInfProof (⇐)
↳10 AND
    ↳11 IDP
        ↳12 IDPNonInfProof (⇐)
        ↳13 AND
            ↳14 IDP
                ↳15 IDependencyGraphProof (⇔)
                ↳16 IDP
                ↳17 IDPNonInfProof (⇐)
                ↳18 AND
                    ↳19 IDP
                        ↳20 IDependencyGraphProof (⇔)
                        ↳21 IDP
                        ↳22 IDPNonInfProof (⇐)
                        ↳23 AND
                            ↳24 IDP
                                ↳25 IDependencyGraphProof (⇔)
                                ↳26 TRUE
                            ↳27 IDP
                                ↳28 IDependencyGraphProof (⇔)
                                ↳29 TRUE
                    ↳30 IDP
                        ↳31 IDPNonInfProof (⇐)
                        ↳32 AND
                            ↳33 IDP
                                ↳34 IDependencyGraphProof (⇔)
                                ↳35 TRUE
                            ↳36 IDP
                                ↳37 IDependencyGraphProof (⇔)
                                ↳38 TRUE
            ↳39 IDP
                ↳40 IDependencyGraphProof (⇔)
                ↳41 IDP
                ↳42 IDPNonInfProof (⇐)
                ↳43 AND
                    ↳44 IDP
                        ↳45 IDependencyGraphProof (⇔)
                        ↳46 TRUE
                    ↳47 IDP
                        ↳48 IDependencyGraphProof (⇔)
                        ↳49 TRUE
    ↳50 IDP
        ↳51 IDependencyGraphProof (⇔)
        ↳52 IDP
        ↳53 IDPNonInfProof (⇐)
        ↳54 AND
            ↳55 IDP
                ↳56 IDependencyGraphProof (⇔)
                ↳57 IDP
                ↳58 IDPNonInfProof (⇐)
                ↳59 AND
                    ↳60 IDP
                        ↳61 IDependencyGraphProof (⇔)
                        ↳62 IDP
                        ↳63 IDPNonInfProof (⇐)
                        ↳64 AND
                            ↳65 IDP
                                ↳66 IDependencyGraphProof (⇔)
                                ↳67 TRUE
                            ↳68 IDP
                                ↳69 IDependencyGraphProof (⇔)
                                ↳70 TRUE
                    ↳71 IDP
                        ↳72 IDependencyGraphProof (⇔)
                        ↳73 TRUE
            ↳74 IDP
                ↳75 IDPNonInfProof (⇐)
                ↳76 AND
                    ↳77 IDP
                        ↳78 IDependencyGraphProof (⇔)
                        ↳79 IDP
                        ↳80 IDPNonInfProof (⇐)
                        ↳81 AND
                            ↳82 IDP
                                ↳83 IDependencyGraphProof (⇔)
                                ↳84 TRUE
                            ↳85 IDP
                                ↳86 IDependencyGraphProof (⇔)
                                ↳87 TRUE
                    ↳88 IDP
                        ↳89 IDependencyGraphProof (⇔)
                        ↳90 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: PastaB13

(1) JBC2FIG (SOUND transformation)

Constructed FIGraph.

(2) Obligation:

FIGraph based on JBC Program:
Graph of 244 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:
Load1222(i79, i85, i69) → Cond_Load1222(i69 >= 0 && i85 > i69 && i79 <= i69, i79, i85, i69)
Cond_Load1222(TRUE, i79, i85, i69) → Load1232(i79, i85, i69)
Load1232(i79, i85, i69) → Cond_Load1232(i85 <= i69 && i79 <= i69, i79, i85, i69)
Cond_Load1232(TRUE, i79, i85, i69) → Load1222(i79, i85, i69)
Load1222(i79, i85, i69) → Cond_Load12221(i85 <= i69 && i79 <= i69 && i69 >= 0 && i79 > i69, i79, i85, i69)
Cond_Load12221(TRUE, i79, i85, i69) → Load1222(i79, i85, i69)
Load1232(i79, i85, i69) → Cond_Load12321(i69 >= 0 && i85 > i69 && i79 <= i69, i79, i85, i69)
Cond_Load12321(TRUE, i79, i85, i69) → Load1222(i79, i85 + -1, i69)
Load1222(i79, i85, i69) → Cond_Load12222(i69 >= 0 && i85 > i69 && i79 <= i69 && i79 > i69, i79, i85, i69)
Cond_Load12222(TRUE, i79, i85, i69) → Load1222(i79, i85 + -1, i69)
Load1232(i79, i85, i69) → Cond_Load12322(i69 >= 0 && i79 > i69, i79, i85, i69)
Cond_Load12322(TRUE, i79, i85, i69) → Load1222(i79 + -1, i85, i69)
Load1222(i79, i85, i69) → Cond_Load12223(i69 >= 0 && i79 > i69, i79, i85, i69)
Cond_Load12223(TRUE, i79, i85, i69) → Load1222(i79 + -1, i85, i69)
The set Q consists of the following terms:
Load1222(x0, x1, x2)
Cond_Load1222(TRUE, x0, x1, x2)
Load1232(x0, x1, x2)
Cond_Load1232(TRUE, x0, x1, x2)
Cond_Load12221(TRUE, x0, x1, x2)
Cond_Load12321(TRUE, x0, x1, x2)
Cond_Load12222(TRUE, x0, x1, x2)
Cond_Load12322(TRUE, x0, x1, x2)
Cond_Load12223(TRUE, x0, x1, x2)

(5) ITRStoIDPProof (EQUIVALENT transformation)

Added dependency pairs

(6) Obligation:

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


The following domains are used:

Boolean, Integer


The ITRS R consists of the following rules:
Load1222(i79, i85, i69) → Cond_Load1222(i69 >= 0 && i85 > i69 && i79 <= i69, i79, i85, i69)
Cond_Load1222(TRUE, i79, i85, i69) → Load1232(i79, i85, i69)
Load1232(i79, i85, i69) → Cond_Load1232(i85 <= i69 && i79 <= i69, i79, i85, i69)
Cond_Load1232(TRUE, i79, i85, i69) → Load1222(i79, i85, i69)
Load1222(i79, i85, i69) → Cond_Load12221(i85 <= i69 && i79 <= i69 && i69 >= 0 && i79 > i69, i79, i85, i69)
Cond_Load12221(TRUE, i79, i85, i69) → Load1222(i79, i85, i69)
Load1232(i79, i85, i69) → Cond_Load12321(i69 >= 0 && i85 > i69 && i79 <= i69, i79, i85, i69)
Cond_Load12321(TRUE, i79, i85, i69) → Load1222(i79, i85 + -1, i69)
Load1222(i79, i85, i69) → Cond_Load12222(i69 >= 0 && i85 > i69 && i79 <= i69 && i79 > i69, i79, i85, i69)
Cond_Load12222(TRUE, i79, i85, i69) → Load1222(i79, i85 + -1, i69)
Load1232(i79, i85, i69) → Cond_Load12322(i69 >= 0 && i79 > i69, i79, i85, i69)
Cond_Load12322(TRUE, i79, i85, i69) → Load1222(i79 + -1, i85, i69)
Load1222(i79, i85, i69) → Cond_Load12223(i69 >= 0 && i79 > i69, i79, i85, i69)
Cond_Load12223(TRUE, i79, i85, i69) → Load1222(i79 + -1, i85, i69)

The integer pair graph contains the following rules and edges:
(0): LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(i69[0] >= 0 && i85[0] > i69[0] && i79[0] <= i69[0], i79[0], i85[0], i69[0])
(1): COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1])
(2): LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(i85[2] <= i69[2] && i79[2] <= i69[2], i79[2], i85[2], i69[2])
(3): COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3])
(4): LOAD1222(i79[4], i85[4], i69[4]) → COND_LOAD12221(i85[4] <= i69[4] && i79[4] <= i69[4] && i69[4] >= 0 && i79[4] > i69[4], i79[4], i85[4], i69[4])
(5): COND_LOAD12221(TRUE, i79[5], i85[5], i69[5]) → LOAD1222(i79[5], i85[5], i69[5])
(6): LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(i69[6] >= 0 && i85[6] > i69[6] && i79[6] <= i69[6], i79[6], i85[6], i69[6])
(7): COND_LOAD12321(TRUE, i79[7], i85[7], i69[7]) → LOAD1222(i79[7], i85[7] + -1, i69[7])
(8): LOAD1222(i79[8], i85[8], i69[8]) → COND_LOAD12222(i69[8] >= 0 && i85[8] > i69[8] && i79[8] <= i69[8] && i79[8] > i69[8], i79[8], i85[8], i69[8])
(9): COND_LOAD12222(TRUE, i79[9], i85[9], i69[9]) → LOAD1222(i79[9], i85[9] + -1, i69[9])
(10): LOAD1232(i79[10], i85[10], i69[10]) → COND_LOAD12322(i69[10] >= 0 && i79[10] > i69[10], i79[10], i85[10], i69[10])
(11): COND_LOAD12322(TRUE, i79[11], i85[11], i69[11]) → LOAD1222(i79[11] + -1, i85[11], i69[11])
(12): LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(i69[12] >= 0 && i79[12] > i69[12], i79[12], i85[12], i69[12])
(13): COND_LOAD12223(TRUE, i79[13], i85[13], i69[13]) → LOAD1222(i79[13] + -1, i85[13], i69[13])

(0) -> (1), if ((i79[0] →* i79[1])∧(i85[0] →* i85[1])∧(i69[0] →* i69[1])∧(i69[0] >= 0 && i85[0] > i69[0] && i79[0] <= i69[0] →* TRUE))


(1) -> (2), if ((i79[1] →* i79[2])∧(i69[1] →* i69[2])∧(i85[1] →* i85[2]))


(1) -> (6), if ((i79[1] →* i79[6])∧(i85[1] →* i85[6])∧(i69[1] →* i69[6]))


(1) -> (10), if ((i69[1] →* i69[10])∧(i79[1] →* i79[10])∧(i85[1] →* i85[10]))


(2) -> (3), if ((i85[2] →* i85[3])∧(i69[2] →* i69[3])∧(i85[2] <= i69[2] && i79[2] <= i69[2] →* TRUE)∧(i79[2] →* i79[3]))


(3) -> (0), if ((i79[3] →* i79[0])∧(i69[3] →* i69[0])∧(i85[3] →* i85[0]))


(3) -> (4), if ((i69[3] →* i69[4])∧(i85[3] →* i85[4])∧(i79[3] →* i79[4]))


(3) -> (8), if ((i69[3] →* i69[8])∧(i79[3] →* i79[8])∧(i85[3] →* i85[8]))


(3) -> (12), if ((i85[3] →* i85[12])∧(i69[3] →* i69[12])∧(i79[3] →* i79[12]))


(4) -> (5), if ((i85[4] <= i69[4] && i79[4] <= i69[4] && i69[4] >= 0 && i79[4] > i69[4] →* TRUE)∧(i85[4] →* i85[5])∧(i69[4] →* i69[5])∧(i79[4] →* i79[5]))


(5) -> (0), if ((i85[5] →* i85[0])∧(i69[5] →* i69[0])∧(i79[5] →* i79[0]))


(5) -> (4), if ((i85[5] →* i85[4])∧(i69[5] →* i69[4])∧(i79[5] →* i79[4]))


(5) -> (8), if ((i79[5] →* i79[8])∧(i69[5] →* i69[8])∧(i85[5] →* i85[8]))


(5) -> (12), if ((i85[5] →* i85[12])∧(i69[5] →* i69[12])∧(i79[5] →* i79[12]))


(6) -> (7), if ((i85[6] →* i85[7])∧(i69[6] >= 0 && i85[6] > i69[6] && i79[6] <= i69[6] →* TRUE)∧(i69[6] →* i69[7])∧(i79[6] →* i79[7]))


(7) -> (0), if ((i85[7] + -1 →* i85[0])∧(i79[7] →* i79[0])∧(i69[7] →* i69[0]))


(7) -> (4), if ((i79[7] →* i79[4])∧(i85[7] + -1 →* i85[4])∧(i69[7] →* i69[4]))


(7) -> (8), if ((i79[7] →* i79[8])∧(i69[7] →* i69[8])∧(i85[7] + -1 →* i85[8]))


(7) -> (12), if ((i79[7] →* i79[12])∧(i69[7] →* i69[12])∧(i85[7] + -1 →* i85[12]))


(8) -> (9), if ((i85[8] →* i85[9])∧(i69[8] >= 0 && i85[8] > i69[8] && i79[8] <= i69[8] && i79[8] > i69[8] →* TRUE)∧(i79[8] →* i79[9])∧(i69[8] →* i69[9]))


(9) -> (0), if ((i69[9] →* i69[0])∧(i79[9] →* i79[0])∧(i85[9] + -1 →* i85[0]))


(9) -> (4), if ((i85[9] + -1 →* i85[4])∧(i79[9] →* i79[4])∧(i69[9] →* i69[4]))


(9) -> (8), if ((i69[9] →* i69[8])∧(i85[9] + -1 →* i85[8])∧(i79[9] →* i79[8]))


(9) -> (12), if ((i69[9] →* i69[12])∧(i85[9] + -1 →* i85[12])∧(i79[9] →* i79[12]))


(10) -> (11), if ((i85[10] →* i85[11])∧(i69[10] >= 0 && i79[10] > i69[10] →* TRUE)∧(i69[10] →* i69[11])∧(i79[10] →* i79[11]))


(11) -> (0), if ((i79[11] + -1 →* i79[0])∧(i85[11] →* i85[0])∧(i69[11] →* i69[0]))


(11) -> (4), if ((i69[11] →* i69[4])∧(i79[11] + -1 →* i79[4])∧(i85[11] →* i85[4]))


(11) -> (8), if ((i85[11] →* i85[8])∧(i79[11] + -1 →* i79[8])∧(i69[11] →* i69[8]))


(11) -> (12), if ((i79[11] + -1 →* i79[12])∧(i85[11] →* i85[12])∧(i69[11] →* i69[12]))


(12) -> (13), if ((i85[12] →* i85[13])∧(i69[12] →* i69[13])∧(i79[12] →* i79[13])∧(i69[12] >= 0 && i79[12] > i69[12] →* TRUE))


(13) -> (0), if ((i69[13] →* i69[0])∧(i79[13] + -1 →* i79[0])∧(i85[13] →* i85[0]))


(13) -> (4), if ((i79[13] + -1 →* i79[4])∧(i69[13] →* i69[4])∧(i85[13] →* i85[4]))


(13) -> (8), if ((i85[13] →* i85[8])∧(i69[13] →* i69[8])∧(i79[13] + -1 →* i79[8]))


(13) -> (12), if ((i69[13] →* i69[12])∧(i85[13] →* i85[12])∧(i79[13] + -1 →* i79[12]))



The set Q consists of the following terms:
Load1222(x0, x1, x2)
Cond_Load1222(TRUE, x0, x1, x2)
Load1232(x0, x1, x2)
Cond_Load1232(TRUE, x0, x1, x2)
Cond_Load12221(TRUE, x0, x1, x2)
Cond_Load12321(TRUE, x0, x1, x2)
Cond_Load12222(TRUE, x0, x1, x2)
Cond_Load12322(TRUE, x0, x1, x2)
Cond_Load12223(TRUE, x0, x1, x2)

(7) UsableRulesProof (EQUIVALENT transformation)

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

(8) Obligation:

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


The following domains are used:

Boolean, Integer


R is empty.

The integer pair graph contains the following rules and edges:
(0): LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(i69[0] >= 0 && i85[0] > i69[0] && i79[0] <= i69[0], i79[0], i85[0], i69[0])
(1): COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1])
(2): LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(i85[2] <= i69[2] && i79[2] <= i69[2], i79[2], i85[2], i69[2])
(3): COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3])
(4): LOAD1222(i79[4], i85[4], i69[4]) → COND_LOAD12221(i85[4] <= i69[4] && i79[4] <= i69[4] && i69[4] >= 0 && i79[4] > i69[4], i79[4], i85[4], i69[4])
(5): COND_LOAD12221(TRUE, i79[5], i85[5], i69[5]) → LOAD1222(i79[5], i85[5], i69[5])
(6): LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(i69[6] >= 0 && i85[6] > i69[6] && i79[6] <= i69[6], i79[6], i85[6], i69[6])
(7): COND_LOAD12321(TRUE, i79[7], i85[7], i69[7]) → LOAD1222(i79[7], i85[7] + -1, i69[7])
(8): LOAD1222(i79[8], i85[8], i69[8]) → COND_LOAD12222(i69[8] >= 0 && i85[8] > i69[8] && i79[8] <= i69[8] && i79[8] > i69[8], i79[8], i85[8], i69[8])
(9): COND_LOAD12222(TRUE, i79[9], i85[9], i69[9]) → LOAD1222(i79[9], i85[9] + -1, i69[9])
(10): LOAD1232(i79[10], i85[10], i69[10]) → COND_LOAD12322(i69[10] >= 0 && i79[10] > i69[10], i79[10], i85[10], i69[10])
(11): COND_LOAD12322(TRUE, i79[11], i85[11], i69[11]) → LOAD1222(i79[11] + -1, i85[11], i69[11])
(12): LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(i69[12] >= 0 && i79[12] > i69[12], i79[12], i85[12], i69[12])
(13): COND_LOAD12223(TRUE, i79[13], i85[13], i69[13]) → LOAD1222(i79[13] + -1, i85[13], i69[13])

(0) -> (1), if ((i79[0] →* i79[1])∧(i85[0] →* i85[1])∧(i69[0] →* i69[1])∧(i69[0] >= 0 && i85[0] > i69[0] && i79[0] <= i69[0] →* TRUE))


(1) -> (2), if ((i79[1] →* i79[2])∧(i69[1] →* i69[2])∧(i85[1] →* i85[2]))


(1) -> (6), if ((i79[1] →* i79[6])∧(i85[1] →* i85[6])∧(i69[1] →* i69[6]))


(1) -> (10), if ((i69[1] →* i69[10])∧(i79[1] →* i79[10])∧(i85[1] →* i85[10]))


(2) -> (3), if ((i85[2] →* i85[3])∧(i69[2] →* i69[3])∧(i85[2] <= i69[2] && i79[2] <= i69[2] →* TRUE)∧(i79[2] →* i79[3]))


(3) -> (0), if ((i79[3] →* i79[0])∧(i69[3] →* i69[0])∧(i85[3] →* i85[0]))


(3) -> (4), if ((i69[3] →* i69[4])∧(i85[3] →* i85[4])∧(i79[3] →* i79[4]))


(3) -> (8), if ((i69[3] →* i69[8])∧(i79[3] →* i79[8])∧(i85[3] →* i85[8]))


(3) -> (12), if ((i85[3] →* i85[12])∧(i69[3] →* i69[12])∧(i79[3] →* i79[12]))


(4) -> (5), if ((i85[4] <= i69[4] && i79[4] <= i69[4] && i69[4] >= 0 && i79[4] > i69[4] →* TRUE)∧(i85[4] →* i85[5])∧(i69[4] →* i69[5])∧(i79[4] →* i79[5]))


(5) -> (0), if ((i85[5] →* i85[0])∧(i69[5] →* i69[0])∧(i79[5] →* i79[0]))


(5) -> (4), if ((i85[5] →* i85[4])∧(i69[5] →* i69[4])∧(i79[5] →* i79[4]))


(5) -> (8), if ((i79[5] →* i79[8])∧(i69[5] →* i69[8])∧(i85[5] →* i85[8]))


(5) -> (12), if ((i85[5] →* i85[12])∧(i69[5] →* i69[12])∧(i79[5] →* i79[12]))


(6) -> (7), if ((i85[6] →* i85[7])∧(i69[6] >= 0 && i85[6] > i69[6] && i79[6] <= i69[6] →* TRUE)∧(i69[6] →* i69[7])∧(i79[6] →* i79[7]))


(7) -> (0), if ((i85[7] + -1 →* i85[0])∧(i79[7] →* i79[0])∧(i69[7] →* i69[0]))


(7) -> (4), if ((i79[7] →* i79[4])∧(i85[7] + -1 →* i85[4])∧(i69[7] →* i69[4]))


(7) -> (8), if ((i79[7] →* i79[8])∧(i69[7] →* i69[8])∧(i85[7] + -1 →* i85[8]))


(7) -> (12), if ((i79[7] →* i79[12])∧(i69[7] →* i69[12])∧(i85[7] + -1 →* i85[12]))


(8) -> (9), if ((i85[8] →* i85[9])∧(i69[8] >= 0 && i85[8] > i69[8] && i79[8] <= i69[8] && i79[8] > i69[8] →* TRUE)∧(i79[8] →* i79[9])∧(i69[8] →* i69[9]))


(9) -> (0), if ((i69[9] →* i69[0])∧(i79[9] →* i79[0])∧(i85[9] + -1 →* i85[0]))


(9) -> (4), if ((i85[9] + -1 →* i85[4])∧(i79[9] →* i79[4])∧(i69[9] →* i69[4]))


(9) -> (8), if ((i69[9] →* i69[8])∧(i85[9] + -1 →* i85[8])∧(i79[9] →* i79[8]))


(9) -> (12), if ((i69[9] →* i69[12])∧(i85[9] + -1 →* i85[12])∧(i79[9] →* i79[12]))


(10) -> (11), if ((i85[10] →* i85[11])∧(i69[10] >= 0 && i79[10] > i69[10] →* TRUE)∧(i69[10] →* i69[11])∧(i79[10] →* i79[11]))


(11) -> (0), if ((i79[11] + -1 →* i79[0])∧(i85[11] →* i85[0])∧(i69[11] →* i69[0]))


(11) -> (4), if ((i69[11] →* i69[4])∧(i79[11] + -1 →* i79[4])∧(i85[11] →* i85[4]))


(11) -> (8), if ((i85[11] →* i85[8])∧(i79[11] + -1 →* i79[8])∧(i69[11] →* i69[8]))


(11) -> (12), if ((i79[11] + -1 →* i79[12])∧(i85[11] →* i85[12])∧(i69[11] →* i69[12]))


(12) -> (13), if ((i85[12] →* i85[13])∧(i69[12] →* i69[13])∧(i79[12] →* i79[13])∧(i69[12] >= 0 && i79[12] > i69[12] →* TRUE))


(13) -> (0), if ((i69[13] →* i69[0])∧(i79[13] + -1 →* i79[0])∧(i85[13] →* i85[0]))


(13) -> (4), if ((i79[13] + -1 →* i79[4])∧(i69[13] →* i69[4])∧(i85[13] →* i85[4]))


(13) -> (8), if ((i85[13] →* i85[8])∧(i69[13] →* i69[8])∧(i79[13] + -1 →* i79[8]))


(13) -> (12), if ((i69[13] →* i69[12])∧(i85[13] →* i85[12])∧(i79[13] + -1 →* i79[12]))



The set Q consists of the following terms:
Load1222(x0, x1, x2)
Cond_Load1222(TRUE, x0, x1, x2)
Load1232(x0, x1, x2)
Cond_Load1232(TRUE, x0, x1, x2)
Cond_Load12221(TRUE, x0, x1, x2)
Cond_Load12321(TRUE, x0, x1, x2)
Cond_Load12222(TRUE, x0, x1, x2)
Cond_Load12322(TRUE, x0, x1, x2)
Cond_Load12223(TRUE, x0, x1, x2)

(9) IDPNonInfProof (SOUND transformation)

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


For Pair LOAD1222(i79, i85, i69) → COND_LOAD1222(&&(&&(>=(i69, 0), >(i85, i69)), <=(i79, i69)), i79, i85, i69) the following chains were created:
  • We consider the chain LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]), COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1]) which results in the following constraint:

    (1)    (i79[0]=i79[1]∧i85[0]=i85[1]∧i69[0]=i69[1]∧&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0]))=TRUE ⇒ LOAD1222(i79[0], i85[0], i69[0])≥NonInfC∧LOAD1222(i79[0], i85[0], i69[0])≥COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])∧(UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥))



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

    (2)    (<=(i79[0], i69[0])=TRUE∧>=(i69[0], 0)=TRUE∧>(i85[0], i69[0])=TRUE ⇒ LOAD1222(i79[0], i85[0], i69[0])≥NonInfC∧LOAD1222(i79[0], i85[0], i69[0])≥COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])∧(UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥))



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

    (3)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] + [-1] + [-1]i69[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)bni_50 + (-1)Bound*bni_50] + [(-1)bni_50]i69[0] ≥ 0∧[(-1)bso_51] ≥ 0)



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

    (4)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] + [-1] + [-1]i69[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)bni_50 + (-1)Bound*bni_50] + [(-1)bni_50]i69[0] ≥ 0∧[(-1)bso_51] ≥ 0)



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

    (5)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] + [-1] + [-1]i69[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)bni_50 + (-1)Bound*bni_50] + [(-1)bni_50]i69[0] ≥ 0∧[(-1)bso_51] ≥ 0)



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

    (6)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)bni_50 + (-1)Bound*bni_50] + [(-1)bni_50]i69[0] ≥ 0∧[(-1)bso_51] ≥ 0)



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

    (7)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)bni_50 + (-1)Bound*bni_50] + [(-1)bni_50]i69[0] ≥ 0∧[(-1)bso_51] ≥ 0)


    (8)    (i69[0] + i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)bni_50 + (-1)Bound*bni_50] + [(-1)bni_50]i69[0] ≥ 0∧[(-1)bso_51] ≥ 0)



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

    (9)    (i69[0] ≥ 0∧i79[0] + i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)bni_50 + (-1)Bound*bni_50] + [(-1)bni_50]i79[0] + [(-1)bni_50]i69[0] ≥ 0∧[(-1)bso_51] ≥ 0)







For Pair COND_LOAD1222(TRUE, i79, i85, i69) → LOAD1232(i79, i85, i69) the following chains were created:
  • We consider the chain COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1]), LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2]) which results in the following constraint:

    (10)    (i79[1]=i79[2]∧i69[1]=i69[2]∧i85[1]=i85[2] ⇒ COND_LOAD1222(TRUE, i79[1], i85[1], i69[1])≥NonInfC∧COND_LOAD1222(TRUE, i79[1], i85[1], i69[1])≥LOAD1232(i79[1], i85[1], i69[1])∧(UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥))



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

    (11)    (COND_LOAD1222(TRUE, i79[1], i85[1], i69[1])≥NonInfC∧COND_LOAD1222(TRUE, i79[1], i85[1], i69[1])≥LOAD1232(i79[1], i85[1], i69[1])∧(UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥))



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

    (12)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_53] ≥ 0)



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

    (13)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_53] ≥ 0)



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

    (14)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_53] ≥ 0)



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

    (15)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_53] ≥ 0)



  • We consider the chain COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1]), LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6]) which results in the following constraint:

    (16)    (i79[1]=i79[6]∧i85[1]=i85[6]∧i69[1]=i69[6] ⇒ COND_LOAD1222(TRUE, i79[1], i85[1], i69[1])≥NonInfC∧COND_LOAD1222(TRUE, i79[1], i85[1], i69[1])≥LOAD1232(i79[1], i85[1], i69[1])∧(UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥))



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

    (17)    (COND_LOAD1222(TRUE, i79[1], i85[1], i69[1])≥NonInfC∧COND_LOAD1222(TRUE, i79[1], i85[1], i69[1])≥LOAD1232(i79[1], i85[1], i69[1])∧(UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥))



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

    (18)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_53] ≥ 0)



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

    (19)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_53] ≥ 0)



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

    (20)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_53] ≥ 0)



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

    (21)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_53] ≥ 0)



  • We consider the chain COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1]), LOAD1232(i79[10], i85[10], i69[10]) → COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10]) which results in the following constraint:

    (22)    (i69[1]=i69[10]∧i79[1]=i79[10]∧i85[1]=i85[10] ⇒ COND_LOAD1222(TRUE, i79[1], i85[1], i69[1])≥NonInfC∧COND_LOAD1222(TRUE, i79[1], i85[1], i69[1])≥LOAD1232(i79[1], i85[1], i69[1])∧(UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥))



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

    (23)    (COND_LOAD1222(TRUE, i79[1], i85[1], i69[1])≥NonInfC∧COND_LOAD1222(TRUE, i79[1], i85[1], i69[1])≥LOAD1232(i79[1], i85[1], i69[1])∧(UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥))



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

    (24)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_53] ≥ 0)



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

    (25)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_53] ≥ 0)



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

    (26)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_53] ≥ 0)



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

    (27)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_53] ≥ 0)







For Pair LOAD1232(i79, i85, i69) → COND_LOAD1232(&&(<=(i85, i69), <=(i79, i69)), i79, i85, i69) the following chains were created:
  • We consider the chain LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2]), COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3]) which results in the following constraint:

    (28)    (i85[2]=i85[3]∧i69[2]=i69[3]∧&&(<=(i85[2], i69[2]), <=(i79[2], i69[2]))=TRUE∧i79[2]=i79[3] ⇒ LOAD1232(i79[2], i85[2], i69[2])≥NonInfC∧LOAD1232(i79[2], i85[2], i69[2])≥COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])∧(UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥))



    We simplified constraint (28) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (29)    (<=(i85[2], i69[2])=TRUE∧<=(i79[2], i69[2])=TRUE ⇒ LOAD1232(i79[2], i85[2], i69[2])≥NonInfC∧LOAD1232(i79[2], i85[2], i69[2])≥COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])∧(UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥))



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

    (30)    (i69[2] + [-1]i85[2] ≥ 0∧i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_54 + (-1)Bound*bni_54] + [(-1)bni_54]i69[2] ≥ 0∧[(-1)bso_55] ≥ 0)



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

    (31)    (i69[2] + [-1]i85[2] ≥ 0∧i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_54 + (-1)Bound*bni_54] + [(-1)bni_54]i69[2] ≥ 0∧[(-1)bso_55] ≥ 0)



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

    (32)    (i69[2] + [-1]i85[2] ≥ 0∧i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_54 + (-1)Bound*bni_54] + [(-1)bni_54]i69[2] ≥ 0∧[(-1)bso_55] ≥ 0)



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

    (33)    (i69[2] ≥ 0∧i85[2] + i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_54 + (-1)Bound*bni_54] + [(-1)bni_54]i85[2] + [(-1)bni_54]i69[2] ≥ 0∧[(-1)bso_55] ≥ 0)



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

    (34)    (i69[2] ≥ 0∧i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_54 + (-1)Bound*bni_54] + [(-1)bni_54]i85[2] + [(-1)bni_54]i69[2] ≥ 0∧[(-1)bso_55] ≥ 0)



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

    (35)    (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_54 + (-1)Bound*bni_54] + [bni_54]i85[2] + [(-1)bni_54]i69[2] ≥ 0∧[(-1)bso_55] ≥ 0)


    (36)    (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_54 + (-1)Bound*bni_54] + [(-1)bni_54]i85[2] + [(-1)bni_54]i69[2] ≥ 0∧[(-1)bso_55] ≥ 0)







For Pair COND_LOAD1232(TRUE, i79, i85, i69) → LOAD1222(i79, i85, i69) the following chains were created:
  • We consider the chain COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3]), LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]) which results in the following constraint:

    (37)    (i79[3]=i79[0]∧i69[3]=i69[0]∧i85[3]=i85[0] ⇒ COND_LOAD1232(TRUE, i79[3], i85[3], i69[3])≥NonInfC∧COND_LOAD1232(TRUE, i79[3], i85[3], i69[3])≥LOAD1222(i79[3], i85[3], i69[3])∧(UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥))



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

    (38)    (COND_LOAD1232(TRUE, i79[3], i85[3], i69[3])≥NonInfC∧COND_LOAD1232(TRUE, i79[3], i85[3], i69[3])≥LOAD1222(i79[3], i85[3], i69[3])∧(UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥))



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

    (39)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bso_57] ≥ 0)



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

    (40)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bso_57] ≥ 0)



    We simplified constraint (40) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (41)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bso_57] ≥ 0)



    We simplified constraint (41) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

    (42)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_57] ≥ 0)



  • We consider the chain COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3]), LOAD1222(i79[4], i85[4], i69[4]) → COND_LOAD12221(&&(&&(&&(<=(i85[4], i69[4]), <=(i79[4], i69[4])), >=(i69[4], 0)), >(i79[4], i69[4])), i79[4], i85[4], i69[4]) which results in the following constraint:

    (43)    (i69[3]=i69[4]∧i85[3]=i85[4]∧i79[3]=i79[4] ⇒ COND_LOAD1232(TRUE, i79[3], i85[3], i69[3])≥NonInfC∧COND_LOAD1232(TRUE, i79[3], i85[3], i69[3])≥LOAD1222(i79[3], i85[3], i69[3])∧(UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥))



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

    (44)    (COND_LOAD1232(TRUE, i79[3], i85[3], i69[3])≥NonInfC∧COND_LOAD1232(TRUE, i79[3], i85[3], i69[3])≥LOAD1222(i79[3], i85[3], i69[3])∧(UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥))



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

    (45)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bso_57] ≥ 0)



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

    (46)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bso_57] ≥ 0)



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

    (47)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bso_57] ≥ 0)



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

    (48)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_57] ≥ 0)



  • We consider the chain COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3]), LOAD1222(i79[8], i85[8], i69[8]) → COND_LOAD12222(&&(&&(&&(>=(i69[8], 0), >(i85[8], i69[8])), <=(i79[8], i69[8])), >(i79[8], i69[8])), i79[8], i85[8], i69[8]) which results in the following constraint:

    (49)    (i69[3]=i69[8]∧i79[3]=i79[8]∧i85[3]=i85[8] ⇒ COND_LOAD1232(TRUE, i79[3], i85[3], i69[3])≥NonInfC∧COND_LOAD1232(TRUE, i79[3], i85[3], i69[3])≥LOAD1222(i79[3], i85[3], i69[3])∧(UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥))



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

    (50)    (COND_LOAD1232(TRUE, i79[3], i85[3], i69[3])≥NonInfC∧COND_LOAD1232(TRUE, i79[3], i85[3], i69[3])≥LOAD1222(i79[3], i85[3], i69[3])∧(UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥))



    We simplified constraint (50) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (51)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bso_57] ≥ 0)



    We simplified constraint (51) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (52)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bso_57] ≥ 0)



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

    (53)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bso_57] ≥ 0)



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

    (54)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_57] ≥ 0)



  • We consider the chain COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3]), LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12]) which results in the following constraint:

    (55)    (i85[3]=i85[12]∧i69[3]=i69[12]∧i79[3]=i79[12] ⇒ COND_LOAD1232(TRUE, i79[3], i85[3], i69[3])≥NonInfC∧COND_LOAD1232(TRUE, i79[3], i85[3], i69[3])≥LOAD1222(i79[3], i85[3], i69[3])∧(UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥))



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

    (56)    (COND_LOAD1232(TRUE, i79[3], i85[3], i69[3])≥NonInfC∧COND_LOAD1232(TRUE, i79[3], i85[3], i69[3])≥LOAD1222(i79[3], i85[3], i69[3])∧(UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥))



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

    (57)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bso_57] ≥ 0)



    We simplified constraint (57) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (58)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bso_57] ≥ 0)



    We simplified constraint (58) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (59)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bso_57] ≥ 0)



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

    (60)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_57] ≥ 0)







For Pair LOAD1222(i79, i85, i69) → COND_LOAD12221(&&(&&(&&(<=(i85, i69), <=(i79, i69)), >=(i69, 0)), >(i79, i69)), i79, i85, i69) the following chains were created:
  • We consider the chain LOAD1222(i79[4], i85[4], i69[4]) → COND_LOAD12221(&&(&&(&&(<=(i85[4], i69[4]), <=(i79[4], i69[4])), >=(i69[4], 0)), >(i79[4], i69[4])), i79[4], i85[4], i69[4]), COND_LOAD12221(TRUE, i79[5], i85[5], i69[5]) → LOAD1222(i79[5], i85[5], i69[5]) which results in the following constraint:

    (61)    (&&(&&(&&(<=(i85[4], i69[4]), <=(i79[4], i69[4])), >=(i69[4], 0)), >(i79[4], i69[4]))=TRUE∧i85[4]=i85[5]∧i69[4]=i69[5]∧i79[4]=i79[5] ⇒ LOAD1222(i79[4], i85[4], i69[4])≥NonInfC∧LOAD1222(i79[4], i85[4], i69[4])≥COND_LOAD12221(&&(&&(&&(<=(i85[4], i69[4]), <=(i79[4], i69[4])), >=(i69[4], 0)), >(i79[4], i69[4])), i79[4], i85[4], i69[4])∧(UIncreasing(COND_LOAD12221(&&(&&(&&(<=(i85[4], i69[4]), <=(i79[4], i69[4])), >=(i69[4], 0)), >(i79[4], i69[4])), i79[4], i85[4], i69[4])), ≥))



    We simplified constraint (61) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (62)    (>(i79[4], i69[4])=TRUE∧>=(i69[4], 0)=TRUE∧<=(i85[4], i69[4])=TRUE∧<=(i79[4], i69[4])=TRUE ⇒ LOAD1222(i79[4], i85[4], i69[4])≥NonInfC∧LOAD1222(i79[4], i85[4], i69[4])≥COND_LOAD12221(&&(&&(&&(<=(i85[4], i69[4]), <=(i79[4], i69[4])), >=(i69[4], 0)), >(i79[4], i69[4])), i79[4], i85[4], i69[4])∧(UIncreasing(COND_LOAD12221(&&(&&(&&(<=(i85[4], i69[4]), <=(i79[4], i69[4])), >=(i69[4], 0)), >(i79[4], i69[4])), i79[4], i85[4], i69[4])), ≥))



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

    (63)    (i79[4] + [-1] + [-1]i69[4] ≥ 0∧i69[4] ≥ 0∧i69[4] + [-1]i85[4] ≥ 0∧i69[4] + [-1]i79[4] ≥ 0 ⇒ (UIncreasing(COND_LOAD12221(&&(&&(&&(<=(i85[4], i69[4]), <=(i79[4], i69[4])), >=(i69[4], 0)), >(i79[4], i69[4])), i79[4], i85[4], i69[4])), ≥)∧[(-1)bni_58 + (-1)Bound*bni_58] + [(-1)bni_58]i69[4] ≥ 0∧[-1 + (-1)bso_59] ≥ 0)



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

    (64)    (i79[4] + [-1] + [-1]i69[4] ≥ 0∧i69[4] ≥ 0∧i69[4] + [-1]i85[4] ≥ 0∧i69[4] + [-1]i79[4] ≥ 0 ⇒ (UIncreasing(COND_LOAD12221(&&(&&(&&(<=(i85[4], i69[4]), <=(i79[4], i69[4])), >=(i69[4], 0)), >(i79[4], i69[4])), i79[4], i85[4], i69[4])), ≥)∧[(-1)bni_58 + (-1)Bound*bni_58] + [(-1)bni_58]i69[4] ≥ 0∧[-1 + (-1)bso_59] ≥ 0)



    We simplified constraint (64) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (65)    (i79[4] + [-1] + [-1]i69[4] ≥ 0∧i69[4] ≥ 0∧i69[4] + [-1]i85[4] ≥ 0∧i69[4] + [-1]i79[4] ≥ 0 ⇒ (UIncreasing(COND_LOAD12221(&&(&&(&&(<=(i85[4], i69[4]), <=(i79[4], i69[4])), >=(i69[4], 0)), >(i79[4], i69[4])), i79[4], i85[4], i69[4])), ≥)∧[(-1)bni_58 + (-1)Bound*bni_58] + [(-1)bni_58]i69[4] ≥ 0∧[-1 + (-1)bso_59] ≥ 0)



    We solved constraint (65) using rule (IDP_SMT_SPLIT).




For Pair COND_LOAD12221(TRUE, i79, i85, i69) → LOAD1222(i79, i85, i69) the following chains were created:
  • We consider the chain COND_LOAD12221(TRUE, i79[5], i85[5], i69[5]) → LOAD1222(i79[5], i85[5], i69[5]), LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]) which results in the following constraint:

    (66)    (i85[5]=i85[0]∧i69[5]=i69[0]∧i79[5]=i79[0] ⇒ COND_LOAD12221(TRUE, i79[5], i85[5], i69[5])≥NonInfC∧COND_LOAD12221(TRUE, i79[5], i85[5], i69[5])≥LOAD1222(i79[5], i85[5], i69[5])∧(UIncreasing(LOAD1222(i79[5], i85[5], i69[5])), ≥))



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

    (67)    (COND_LOAD12221(TRUE, i79[5], i85[5], i69[5])≥NonInfC∧COND_LOAD12221(TRUE, i79[5], i85[5], i69[5])≥LOAD1222(i79[5], i85[5], i69[5])∧(UIncreasing(LOAD1222(i79[5], i85[5], i69[5])), ≥))



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

    (68)    ((UIncreasing(LOAD1222(i79[5], i85[5], i69[5])), ≥)∧[3 + (-1)bso_61] ≥ 0)



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

    (69)    ((UIncreasing(LOAD1222(i79[5], i85[5], i69[5])), ≥)∧[3 + (-1)bso_61] ≥ 0)



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

    (70)    ((UIncreasing(LOAD1222(i79[5], i85[5], i69[5])), ≥)∧[3 + (-1)bso_61] ≥ 0)



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

    (71)    ((UIncreasing(LOAD1222(i79[5], i85[5], i69[5])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[3 + (-1)bso_61] ≥ 0)



  • We consider the chain COND_LOAD12221(TRUE, i79[5], i85[5], i69[5]) → LOAD1222(i79[5], i85[5], i69[5]), LOAD1222(i79[4], i85[4], i69[4]) → COND_LOAD12221(&&(&&(&&(<=(i85[4], i69[4]), <=(i79[4], i69[4])), >=(i69[4], 0)), >(i79[4], i69[4])), i79[4], i85[4], i69[4]) which results in the following constraint:

    (72)    (i85[5]=i85[4]∧i69[5]=i69[4]∧i79[5]=i79[4] ⇒ COND_LOAD12221(TRUE, i79[5], i85[5], i69[5])≥NonInfC∧COND_LOAD12221(TRUE, i79[5], i85[5], i69[5])≥LOAD1222(i79[5], i85[5], i69[5])∧(UIncreasing(LOAD1222(i79[5], i85[5], i69[5])), ≥))



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

    (73)    (COND_LOAD12221(TRUE, i79[5], i85[5], i69[5])≥NonInfC∧COND_LOAD12221(TRUE, i79[5], i85[5], i69[5])≥LOAD1222(i79[5], i85[5], i69[5])∧(UIncreasing(LOAD1222(i79[5], i85[5], i69[5])), ≥))



    We simplified constraint (73) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (74)    ((UIncreasing(LOAD1222(i79[5], i85[5], i69[5])), ≥)∧[3 + (-1)bso_61] ≥ 0)



    We simplified constraint (74) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (75)    ((UIncreasing(LOAD1222(i79[5], i85[5], i69[5])), ≥)∧[3 + (-1)bso_61] ≥ 0)



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

    (76)    ((UIncreasing(LOAD1222(i79[5], i85[5], i69[5])), ≥)∧[3 + (-1)bso_61] ≥ 0)



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

    (77)    ((UIncreasing(LOAD1222(i79[5], i85[5], i69[5])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[3 + (-1)bso_61] ≥ 0)



  • We consider the chain COND_LOAD12221(TRUE, i79[5], i85[5], i69[5]) → LOAD1222(i79[5], i85[5], i69[5]), LOAD1222(i79[8], i85[8], i69[8]) → COND_LOAD12222(&&(&&(&&(>=(i69[8], 0), >(i85[8], i69[8])), <=(i79[8], i69[8])), >(i79[8], i69[8])), i79[8], i85[8], i69[8]) which results in the following constraint:

    (78)    (i79[5]=i79[8]∧i69[5]=i69[8]∧i85[5]=i85[8] ⇒ COND_LOAD12221(TRUE, i79[5], i85[5], i69[5])≥NonInfC∧COND_LOAD12221(TRUE, i79[5], i85[5], i69[5])≥LOAD1222(i79[5], i85[5], i69[5])∧(UIncreasing(LOAD1222(i79[5], i85[5], i69[5])), ≥))



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

    (79)    (COND_LOAD12221(TRUE, i79[5], i85[5], i69[5])≥NonInfC∧COND_LOAD12221(TRUE, i79[5], i85[5], i69[5])≥LOAD1222(i79[5], i85[5], i69[5])∧(UIncreasing(LOAD1222(i79[5], i85[5], i69[5])), ≥))



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

    (80)    ((UIncreasing(LOAD1222(i79[5], i85[5], i69[5])), ≥)∧[3 + (-1)bso_61] ≥ 0)



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

    (81)    ((UIncreasing(LOAD1222(i79[5], i85[5], i69[5])), ≥)∧[3 + (-1)bso_61] ≥ 0)



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

    (82)    ((UIncreasing(LOAD1222(i79[5], i85[5], i69[5])), ≥)∧[3 + (-1)bso_61] ≥ 0)



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

    (83)    ((UIncreasing(LOAD1222(i79[5], i85[5], i69[5])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[3 + (-1)bso_61] ≥ 0)



  • We consider the chain COND_LOAD12221(TRUE, i79[5], i85[5], i69[5]) → LOAD1222(i79[5], i85[5], i69[5]), LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12]) which results in the following constraint:

    (84)    (i85[5]=i85[12]∧i69[5]=i69[12]∧i79[5]=i79[12] ⇒ COND_LOAD12221(TRUE, i79[5], i85[5], i69[5])≥NonInfC∧COND_LOAD12221(TRUE, i79[5], i85[5], i69[5])≥LOAD1222(i79[5], i85[5], i69[5])∧(UIncreasing(LOAD1222(i79[5], i85[5], i69[5])), ≥))



    We simplified constraint (84) using rule (IV) which results in the following new constraint:

    (85)    (COND_LOAD12221(TRUE, i79[5], i85[5], i69[5])≥NonInfC∧COND_LOAD12221(TRUE, i79[5], i85[5], i69[5])≥LOAD1222(i79[5], i85[5], i69[5])∧(UIncreasing(LOAD1222(i79[5], i85[5], i69[5])), ≥))



    We simplified constraint (85) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (86)    ((UIncreasing(LOAD1222(i79[5], i85[5], i69[5])), ≥)∧[3 + (-1)bso_61] ≥ 0)



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

    (87)    ((UIncreasing(LOAD1222(i79[5], i85[5], i69[5])), ≥)∧[3 + (-1)bso_61] ≥ 0)



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

    (88)    ((UIncreasing(LOAD1222(i79[5], i85[5], i69[5])), ≥)∧[3 + (-1)bso_61] ≥ 0)



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

    (89)    ((UIncreasing(LOAD1222(i79[5], i85[5], i69[5])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[3 + (-1)bso_61] ≥ 0)







For Pair LOAD1232(i79, i85, i69) → COND_LOAD12321(&&(&&(>=(i69, 0), >(i85, i69)), <=(i79, i69)), i79, i85, i69) the following chains were created:
  • We consider the chain LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6]), COND_LOAD12321(TRUE, i79[7], i85[7], i69[7]) → LOAD1222(i79[7], +(i85[7], -1), i69[7]) which results in the following constraint:

    (90)    (i85[6]=i85[7]∧&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6]))=TRUE∧i69[6]=i69[7]∧i79[6]=i79[7] ⇒ LOAD1232(i79[6], i85[6], i69[6])≥NonInfC∧LOAD1232(i79[6], i85[6], i69[6])≥COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])∧(UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥))



    We simplified constraint (90) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (91)    (<=(i79[6], i69[6])=TRUE∧>=(i69[6], 0)=TRUE∧>(i85[6], i69[6])=TRUE ⇒ LOAD1232(i79[6], i85[6], i69[6])≥NonInfC∧LOAD1232(i79[6], i85[6], i69[6])≥COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])∧(UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥))



    We simplified constraint (91) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (92)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] + [-1] + [-1]i69[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)bni_62 + (-1)Bound*bni_62] + [(-1)bni_62]i69[6] ≥ 0∧[(-1)bso_63] ≥ 0)



    We simplified constraint (92) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (93)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] + [-1] + [-1]i69[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)bni_62 + (-1)Bound*bni_62] + [(-1)bni_62]i69[6] ≥ 0∧[(-1)bso_63] ≥ 0)



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

    (94)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] + [-1] + [-1]i69[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)bni_62 + (-1)Bound*bni_62] + [(-1)bni_62]i69[6] ≥ 0∧[(-1)bso_63] ≥ 0)



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

    (95)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)bni_62 + (-1)Bound*bni_62] + [(-1)bni_62]i69[6] ≥ 0∧[(-1)bso_63] ≥ 0)



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

    (96)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)bni_62 + (-1)Bound*bni_62] + [(-1)bni_62]i69[6] ≥ 0∧[(-1)bso_63] ≥ 0)


    (97)    (i69[6] + i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)bni_62 + (-1)Bound*bni_62] + [(-1)bni_62]i69[6] ≥ 0∧[(-1)bso_63] ≥ 0)



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

    (98)    (i69[6] ≥ 0∧i79[6] + i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)bni_62 + (-1)Bound*bni_62] + [(-1)bni_62]i79[6] + [(-1)bni_62]i69[6] ≥ 0∧[(-1)bso_63] ≥ 0)







For Pair COND_LOAD12321(TRUE, i79, i85, i69) → LOAD1222(i79, +(i85, -1), i69) the following chains were created:
  • We consider the chain LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6]), COND_LOAD12321(TRUE, i79[7], i85[7], i69[7]) → LOAD1222(i79[7], +(i85[7], -1), i69[7]) which results in the following constraint:

    (99)    (i85[6]=i85[7]∧&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6]))=TRUE∧i69[6]=i69[7]∧i79[6]=i79[7] ⇒ COND_LOAD12321(TRUE, i79[7], i85[7], i69[7])≥NonInfC∧COND_LOAD12321(TRUE, i79[7], i85[7], i69[7])≥LOAD1222(i79[7], +(i85[7], -1), i69[7])∧(UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥))



    We simplified constraint (99) using rules (III), (IDP_BOOLEAN) which results in the following new constraint:

    (100)    (<=(i79[6], i69[6])=TRUE∧>=(i69[6], 0)=TRUE∧>(i85[6], i69[6])=TRUE ⇒ COND_LOAD12321(TRUE, i79[6], i85[6], i69[6])≥NonInfC∧COND_LOAD12321(TRUE, i79[6], i85[6], i69[6])≥LOAD1222(i79[6], +(i85[6], -1), i69[6])∧(UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥))



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

    (101)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] + [-1] + [-1]i69[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)bni_64 + (-1)Bound*bni_64] + [(-1)bni_64]i69[6] ≥ 0∧[(-1)bso_65] ≥ 0)



    We simplified constraint (101) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (102)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] + [-1] + [-1]i69[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)bni_64 + (-1)Bound*bni_64] + [(-1)bni_64]i69[6] ≥ 0∧[(-1)bso_65] ≥ 0)



    We simplified constraint (102) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (103)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] + [-1] + [-1]i69[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)bni_64 + (-1)Bound*bni_64] + [(-1)bni_64]i69[6] ≥ 0∧[(-1)bso_65] ≥ 0)



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

    (104)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)bni_64 + (-1)Bound*bni_64] + [(-1)bni_64]i69[6] ≥ 0∧[(-1)bso_65] ≥ 0)



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

    (105)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)bni_64 + (-1)Bound*bni_64] + [(-1)bni_64]i69[6] ≥ 0∧[(-1)bso_65] ≥ 0)


    (106)    (i69[6] + i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)bni_64 + (-1)Bound*bni_64] + [(-1)bni_64]i69[6] ≥ 0∧[(-1)bso_65] ≥ 0)



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

    (107)    (i69[6] ≥ 0∧i79[6] + i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)bni_64 + (-1)Bound*bni_64] + [(-1)bni_64]i79[6] + [(-1)bni_64]i69[6] ≥ 0∧[(-1)bso_65] ≥ 0)







For Pair LOAD1222(i79, i85, i69) → COND_LOAD12222(&&(&&(&&(>=(i69, 0), >(i85, i69)), <=(i79, i69)), >(i79, i69)), i79, i85, i69) the following chains were created:
  • We consider the chain LOAD1222(i79[8], i85[8], i69[8]) → COND_LOAD12222(&&(&&(&&(>=(i69[8], 0), >(i85[8], i69[8])), <=(i79[8], i69[8])), >(i79[8], i69[8])), i79[8], i85[8], i69[8]), COND_LOAD12222(TRUE, i79[9], i85[9], i69[9]) → LOAD1222(i79[9], +(i85[9], -1), i69[9]) which results in the following constraint:

    (108)    (i85[8]=i85[9]∧&&(&&(&&(>=(i69[8], 0), >(i85[8], i69[8])), <=(i79[8], i69[8])), >(i79[8], i69[8]))=TRUE∧i79[8]=i79[9]∧i69[8]=i69[9] ⇒ LOAD1222(i79[8], i85[8], i69[8])≥NonInfC∧LOAD1222(i79[8], i85[8], i69[8])≥COND_LOAD12222(&&(&&(&&(>=(i69[8], 0), >(i85[8], i69[8])), <=(i79[8], i69[8])), >(i79[8], i69[8])), i79[8], i85[8], i69[8])∧(UIncreasing(COND_LOAD12222(&&(&&(&&(>=(i69[8], 0), >(i85[8], i69[8])), <=(i79[8], i69[8])), >(i79[8], i69[8])), i79[8], i85[8], i69[8])), ≥))



    We simplified constraint (108) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (109)    (>(i79[8], i69[8])=TRUE∧<=(i79[8], i69[8])=TRUE∧>=(i69[8], 0)=TRUE∧>(i85[8], i69[8])=TRUE ⇒ LOAD1222(i79[8], i85[8], i69[8])≥NonInfC∧LOAD1222(i79[8], i85[8], i69[8])≥COND_LOAD12222(&&(&&(&&(>=(i69[8], 0), >(i85[8], i69[8])), <=(i79[8], i69[8])), >(i79[8], i69[8])), i79[8], i85[8], i69[8])∧(UIncreasing(COND_LOAD12222(&&(&&(&&(>=(i69[8], 0), >(i85[8], i69[8])), <=(i79[8], i69[8])), >(i79[8], i69[8])), i79[8], i85[8], i69[8])), ≥))



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

    (110)    (i79[8] + [-1] + [-1]i69[8] ≥ 0∧i69[8] + [-1]i79[8] ≥ 0∧i69[8] ≥ 0∧i85[8] + [-1] + [-1]i69[8] ≥ 0 ⇒ (UIncreasing(COND_LOAD12222(&&(&&(&&(>=(i69[8], 0), >(i85[8], i69[8])), <=(i79[8], i69[8])), >(i79[8], i69[8])), i79[8], i85[8], i69[8])), ≥)∧[(-1)bni_66 + (-1)Bound*bni_66] + [(-1)bni_66]i69[8] ≥ 0∧[-1 + (-1)bso_67] + i85[8] + i79[8] ≥ 0)



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

    (111)    (i79[8] + [-1] + [-1]i69[8] ≥ 0∧i69[8] + [-1]i79[8] ≥ 0∧i69[8] ≥ 0∧i85[8] + [-1] + [-1]i69[8] ≥ 0 ⇒ (UIncreasing(COND_LOAD12222(&&(&&(&&(>=(i69[8], 0), >(i85[8], i69[8])), <=(i79[8], i69[8])), >(i79[8], i69[8])), i79[8], i85[8], i69[8])), ≥)∧[(-1)bni_66 + (-1)Bound*bni_66] + [(-1)bni_66]i69[8] ≥ 0∧[-1 + (-1)bso_67] + i85[8] + i79[8] ≥ 0)



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

    (112)    (i79[8] + [-1] + [-1]i69[8] ≥ 0∧i69[8] + [-1]i79[8] ≥ 0∧i69[8] ≥ 0∧i85[8] + [-1] + [-1]i69[8] ≥ 0 ⇒ (UIncreasing(COND_LOAD12222(&&(&&(&&(>=(i69[8], 0), >(i85[8], i69[8])), <=(i79[8], i69[8])), >(i79[8], i69[8])), i79[8], i85[8], i69[8])), ≥)∧[(-1)bni_66 + (-1)Bound*bni_66] + [(-1)bni_66]i69[8] ≥ 0∧[-1 + (-1)bso_67] + i85[8] + i79[8] ≥ 0)



    We solved constraint (112) using rule (IDP_SMT_SPLIT).




For Pair COND_LOAD12222(TRUE, i79, i85, i69) → LOAD1222(i79, +(i85, -1), i69) the following chains were created:
  • We consider the chain LOAD1222(i79[8], i85[8], i69[8]) → COND_LOAD12222(&&(&&(&&(>=(i69[8], 0), >(i85[8], i69[8])), <=(i79[8], i69[8])), >(i79[8], i69[8])), i79[8], i85[8], i69[8]), COND_LOAD12222(TRUE, i79[9], i85[9], i69[9]) → LOAD1222(i79[9], +(i85[9], -1), i69[9]) which results in the following constraint:

    (113)    (i85[8]=i85[9]∧&&(&&(&&(>=(i69[8], 0), >(i85[8], i69[8])), <=(i79[8], i69[8])), >(i79[8], i69[8]))=TRUE∧i79[8]=i79[9]∧i69[8]=i69[9] ⇒ COND_LOAD12222(TRUE, i79[9], i85[9], i69[9])≥NonInfC∧COND_LOAD12222(TRUE, i79[9], i85[9], i69[9])≥LOAD1222(i79[9], +(i85[9], -1), i69[9])∧(UIncreasing(LOAD1222(i79[9], +(i85[9], -1), i69[9])), ≥))



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

    (114)    (>(i79[8], i69[8])=TRUE∧<=(i79[8], i69[8])=TRUE∧>=(i69[8], 0)=TRUE∧>(i85[8], i69[8])=TRUE ⇒ COND_LOAD12222(TRUE, i79[8], i85[8], i69[8])≥NonInfC∧COND_LOAD12222(TRUE, i79[8], i85[8], i69[8])≥LOAD1222(i79[8], +(i85[8], -1), i69[8])∧(UIncreasing(LOAD1222(i79[9], +(i85[9], -1), i69[9])), ≥))



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

    (115)    (i79[8] + [-1] + [-1]i69[8] ≥ 0∧i69[8] + [-1]i79[8] ≥ 0∧i69[8] ≥ 0∧i85[8] + [-1] + [-1]i69[8] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[9], +(i85[9], -1), i69[9])), ≥)∧[(-2)bni_68 + (-1)Bound*bni_68] + [(-1)bni_68]i69[8] + [(-1)bni_68]i85[8] + [(-1)bni_68]i79[8] ≥ 0∧[-1 + (-1)bso_69] + [-1]i85[8] + [-1]i79[8] ≥ 0)



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

    (116)    (i79[8] + [-1] + [-1]i69[8] ≥ 0∧i69[8] + [-1]i79[8] ≥ 0∧i69[8] ≥ 0∧i85[8] + [-1] + [-1]i69[8] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[9], +(i85[9], -1), i69[9])), ≥)∧[(-2)bni_68 + (-1)Bound*bni_68] + [(-1)bni_68]i69[8] + [(-1)bni_68]i85[8] + [(-1)bni_68]i79[8] ≥ 0∧[-1 + (-1)bso_69] + [-1]i85[8] + [-1]i79[8] ≥ 0)



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

    (117)    (i79[8] + [-1] + [-1]i69[8] ≥ 0∧i69[8] + [-1]i79[8] ≥ 0∧i69[8] ≥ 0∧i85[8] + [-1] + [-1]i69[8] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[9], +(i85[9], -1), i69[9])), ≥)∧[(-2)bni_68 + (-1)Bound*bni_68] + [(-1)bni_68]i69[8] + [(-1)bni_68]i85[8] + [(-1)bni_68]i79[8] ≥ 0∧[-1 + (-1)bso_69] + [-1]i85[8] + [-1]i79[8] ≥ 0)



    We solved constraint (117) using rule (IDP_SMT_SPLIT).




For Pair LOAD1232(i79, i85, i69) → COND_LOAD12322(&&(>=(i69, 0), >(i79, i69)), i79, i85, i69) the following chains were created:
  • We consider the chain LOAD1232(i79[10], i85[10], i69[10]) → COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10]), COND_LOAD12322(TRUE, i79[11], i85[11], i69[11]) → LOAD1222(+(i79[11], -1), i85[11], i69[11]) which results in the following constraint:

    (118)    (i85[10]=i85[11]∧&&(>=(i69[10], 0), >(i79[10], i69[10]))=TRUE∧i69[10]=i69[11]∧i79[10]=i79[11] ⇒ LOAD1232(i79[10], i85[10], i69[10])≥NonInfC∧LOAD1232(i79[10], i85[10], i69[10])≥COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])∧(UIncreasing(COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])), ≥))



    We simplified constraint (118) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (119)    (>=(i69[10], 0)=TRUE∧>(i79[10], i69[10])=TRUE ⇒ LOAD1232(i79[10], i85[10], i69[10])≥NonInfC∧LOAD1232(i79[10], i85[10], i69[10])≥COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])∧(UIncreasing(COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])), ≥))



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

    (120)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])), ≥)∧[(-1)bni_70 + (-1)Bound*bni_70] + [(-1)bni_70]i69[10] ≥ 0∧[(-1)bso_71] ≥ 0)



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

    (121)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])), ≥)∧[(-1)bni_70 + (-1)Bound*bni_70] + [(-1)bni_70]i69[10] ≥ 0∧[(-1)bso_71] ≥ 0)



    We simplified constraint (121) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (122)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])), ≥)∧[(-1)bni_70 + (-1)Bound*bni_70] + [(-1)bni_70]i69[10] ≥ 0∧[(-1)bso_71] ≥ 0)



    We simplified constraint (122) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

    (123)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])), ≥)∧0 = 0∧[(-1)bni_70 + (-1)Bound*bni_70] + [(-1)bni_70]i69[10] ≥ 0∧0 = 0∧[(-1)bso_71] ≥ 0)



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

    (124)    (i69[10] ≥ 0∧i79[10] ≥ 0 ⇒ (UIncreasing(COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])), ≥)∧0 = 0∧[(-1)bni_70 + (-1)Bound*bni_70] + [(-1)bni_70]i69[10] ≥ 0∧0 = 0∧[(-1)bso_71] ≥ 0)







For Pair COND_LOAD12322(TRUE, i79, i85, i69) → LOAD1222(+(i79, -1), i85, i69) the following chains were created:
  • We consider the chain LOAD1232(i79[10], i85[10], i69[10]) → COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10]), COND_LOAD12322(TRUE, i79[11], i85[11], i69[11]) → LOAD1222(+(i79[11], -1), i85[11], i69[11]) which results in the following constraint:

    (125)    (i85[10]=i85[11]∧&&(>=(i69[10], 0), >(i79[10], i69[10]))=TRUE∧i69[10]=i69[11]∧i79[10]=i79[11] ⇒ COND_LOAD12322(TRUE, i79[11], i85[11], i69[11])≥NonInfC∧COND_LOAD12322(TRUE, i79[11], i85[11], i69[11])≥LOAD1222(+(i79[11], -1), i85[11], i69[11])∧(UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥))



    We simplified constraint (125) using rules (III), (IDP_BOOLEAN) which results in the following new constraint:

    (126)    (>=(i69[10], 0)=TRUE∧>(i79[10], i69[10])=TRUE ⇒ COND_LOAD12322(TRUE, i79[10], i85[10], i69[10])≥NonInfC∧COND_LOAD12322(TRUE, i79[10], i85[10], i69[10])≥LOAD1222(+(i79[10], -1), i85[10], i69[10])∧(UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥))



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

    (127)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧[(-1)bni_72 + (-1)Bound*bni_72] + [(-1)bni_72]i69[10] ≥ 0∧[(-1)bso_73] ≥ 0)



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

    (128)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧[(-1)bni_72 + (-1)Bound*bni_72] + [(-1)bni_72]i69[10] ≥ 0∧[(-1)bso_73] ≥ 0)



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

    (129)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧[(-1)bni_72 + (-1)Bound*bni_72] + [(-1)bni_72]i69[10] ≥ 0∧[(-1)bso_73] ≥ 0)



    We simplified constraint (129) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

    (130)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧0 = 0∧[(-1)bni_72 + (-1)Bound*bni_72] + [(-1)bni_72]i69[10] ≥ 0∧0 = 0∧[(-1)bso_73] ≥ 0)



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

    (131)    (i69[10] ≥ 0∧i79[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧0 = 0∧[(-1)bni_72 + (-1)Bound*bni_72] + [(-1)bni_72]i69[10] ≥ 0∧0 = 0∧[(-1)bso_73] ≥ 0)







For Pair LOAD1222(i79, i85, i69) → COND_LOAD12223(&&(>=(i69, 0), >(i79, i69)), i79, i85, i69) the following chains were created:
  • We consider the chain LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12]), COND_LOAD12223(TRUE, i79[13], i85[13], i69[13]) → LOAD1222(+(i79[13], -1), i85[13], i69[13]) which results in the following constraint:

    (132)    (i85[12]=i85[13]∧i69[12]=i69[13]∧i79[12]=i79[13]∧&&(>=(i69[12], 0), >(i79[12], i69[12]))=TRUE ⇒ LOAD1222(i79[12], i85[12], i69[12])≥NonInfC∧LOAD1222(i79[12], i85[12], i69[12])≥COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])∧(UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥))



    We simplified constraint (132) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (133)    (>=(i69[12], 0)=TRUE∧>(i79[12], i69[12])=TRUE ⇒ LOAD1222(i79[12], i85[12], i69[12])≥NonInfC∧LOAD1222(i79[12], i85[12], i69[12])≥COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])∧(UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥))



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

    (134)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥)∧[(-1)bni_74 + (-1)Bound*bni_74] + [(-1)bni_74]i69[12] ≥ 0∧[(-1)bso_75] ≥ 0)



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

    (135)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥)∧[(-1)bni_74 + (-1)Bound*bni_74] + [(-1)bni_74]i69[12] ≥ 0∧[(-1)bso_75] ≥ 0)



    We simplified constraint (135) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (136)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥)∧[(-1)bni_74 + (-1)Bound*bni_74] + [(-1)bni_74]i69[12] ≥ 0∧[(-1)bso_75] ≥ 0)



    We simplified constraint (136) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

    (137)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥)∧0 = 0∧[(-1)bni_74 + (-1)Bound*bni_74] + [(-1)bni_74]i69[12] ≥ 0∧0 = 0∧[(-1)bso_75] ≥ 0)



    We simplified constraint (137) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (138)    (i69[12] ≥ 0∧i79[12] ≥ 0 ⇒ (UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥)∧0 = 0∧[(-1)bni_74 + (-1)Bound*bni_74] + [(-1)bni_74]i69[12] ≥ 0∧0 = 0∧[(-1)bso_75] ≥ 0)







For Pair COND_LOAD12223(TRUE, i79, i85, i69) → LOAD1222(+(i79, -1), i85, i69) the following chains were created:
  • We consider the chain LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12]), COND_LOAD12223(TRUE, i79[13], i85[13], i69[13]) → LOAD1222(+(i79[13], -1), i85[13], i69[13]) which results in the following constraint:

    (139)    (i85[12]=i85[13]∧i69[12]=i69[13]∧i79[12]=i79[13]∧&&(>=(i69[12], 0), >(i79[12], i69[12]))=TRUE ⇒ COND_LOAD12223(TRUE, i79[13], i85[13], i69[13])≥NonInfC∧COND_LOAD12223(TRUE, i79[13], i85[13], i69[13])≥LOAD1222(+(i79[13], -1), i85[13], i69[13])∧(UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥))



    We simplified constraint (139) using rules (III), (IDP_BOOLEAN) which results in the following new constraint:

    (140)    (>=(i69[12], 0)=TRUE∧>(i79[12], i69[12])=TRUE ⇒ COND_LOAD12223(TRUE, i79[12], i85[12], i69[12])≥NonInfC∧COND_LOAD12223(TRUE, i79[12], i85[12], i69[12])≥LOAD1222(+(i79[12], -1), i85[12], i69[12])∧(UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥))



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

    (141)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧[(-1)bni_76 + (-1)Bound*bni_76] + [(-1)bni_76]i69[12] ≥ 0∧[(-1)bso_77] ≥ 0)



    We simplified constraint (141) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (142)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧[(-1)bni_76 + (-1)Bound*bni_76] + [(-1)bni_76]i69[12] ≥ 0∧[(-1)bso_77] ≥ 0)



    We simplified constraint (142) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (143)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧[(-1)bni_76 + (-1)Bound*bni_76] + [(-1)bni_76]i69[12] ≥ 0∧[(-1)bso_77] ≥ 0)



    We simplified constraint (143) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

    (144)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧0 = 0∧[(-1)bni_76 + (-1)Bound*bni_76] + [(-1)bni_76]i69[12] ≥ 0∧0 = 0∧[(-1)bso_77] ≥ 0)



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

    (145)    (i69[12] ≥ 0∧i79[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧0 = 0∧[(-1)bni_76 + (-1)Bound*bni_76] + [(-1)bni_76]i69[12] ≥ 0∧0 = 0∧[(-1)bso_77] ≥ 0)







To summarize, we get the following constraints P≥ for the following pairs.
  • LOAD1222(i79, i85, i69) → COND_LOAD1222(&&(&&(>=(i69, 0), >(i85, i69)), <=(i79, i69)), i79, i85, i69)
    • (i69[0] + i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)bni_50 + (-1)Bound*bni_50] + [(-1)bni_50]i69[0] ≥ 0∧[(-1)bso_51] ≥ 0)
    • (i69[0] ≥ 0∧i79[0] + i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)bni_50 + (-1)Bound*bni_50] + [(-1)bni_50]i79[0] + [(-1)bni_50]i69[0] ≥ 0∧[(-1)bso_51] ≥ 0)

  • COND_LOAD1222(TRUE, i79, i85, i69) → LOAD1232(i79, i85, i69)
    • ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_53] ≥ 0)
    • ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_53] ≥ 0)
    • ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_53] ≥ 0)

  • LOAD1232(i79, i85, i69) → COND_LOAD1232(&&(<=(i85, i69), <=(i79, i69)), i79, i85, i69)
    • (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_54 + (-1)Bound*bni_54] + [bni_54]i85[2] + [(-1)bni_54]i69[2] ≥ 0∧[(-1)bso_55] ≥ 0)
    • (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_54 + (-1)Bound*bni_54] + [(-1)bni_54]i85[2] + [(-1)bni_54]i69[2] ≥ 0∧[(-1)bso_55] ≥ 0)

  • COND_LOAD1232(TRUE, i79, i85, i69) → LOAD1222(i79, i85, i69)
    • ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_57] ≥ 0)
    • ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_57] ≥ 0)
    • ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_57] ≥ 0)
    • ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_57] ≥ 0)

  • LOAD1222(i79, i85, i69) → COND_LOAD12221(&&(&&(&&(<=(i85, i69), <=(i79, i69)), >=(i69, 0)), >(i79, i69)), i79, i85, i69)

  • COND_LOAD12221(TRUE, i79, i85, i69) → LOAD1222(i79, i85, i69)
    • ((UIncreasing(LOAD1222(i79[5], i85[5], i69[5])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[3 + (-1)bso_61] ≥ 0)
    • ((UIncreasing(LOAD1222(i79[5], i85[5], i69[5])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[3 + (-1)bso_61] ≥ 0)
    • ((UIncreasing(LOAD1222(i79[5], i85[5], i69[5])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[3 + (-1)bso_61] ≥ 0)
    • ((UIncreasing(LOAD1222(i79[5], i85[5], i69[5])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[3 + (-1)bso_61] ≥ 0)

  • LOAD1232(i79, i85, i69) → COND_LOAD12321(&&(&&(>=(i69, 0), >(i85, i69)), <=(i79, i69)), i79, i85, i69)
    • (i69[6] + i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)bni_62 + (-1)Bound*bni_62] + [(-1)bni_62]i69[6] ≥ 0∧[(-1)bso_63] ≥ 0)
    • (i69[6] ≥ 0∧i79[6] + i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)bni_62 + (-1)Bound*bni_62] + [(-1)bni_62]i79[6] + [(-1)bni_62]i69[6] ≥ 0∧[(-1)bso_63] ≥ 0)

  • COND_LOAD12321(TRUE, i79, i85, i69) → LOAD1222(i79, +(i85, -1), i69)
    • (i69[6] + i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)bni_64 + (-1)Bound*bni_64] + [(-1)bni_64]i69[6] ≥ 0∧[(-1)bso_65] ≥ 0)
    • (i69[6] ≥ 0∧i79[6] + i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)bni_64 + (-1)Bound*bni_64] + [(-1)bni_64]i79[6] + [(-1)bni_64]i69[6] ≥ 0∧[(-1)bso_65] ≥ 0)

  • LOAD1222(i79, i85, i69) → COND_LOAD12222(&&(&&(&&(>=(i69, 0), >(i85, i69)), <=(i79, i69)), >(i79, i69)), i79, i85, i69)

  • COND_LOAD12222(TRUE, i79, i85, i69) → LOAD1222(i79, +(i85, -1), i69)

  • LOAD1232(i79, i85, i69) → COND_LOAD12322(&&(>=(i69, 0), >(i79, i69)), i79, i85, i69)
    • (i69[10] ≥ 0∧i79[10] ≥ 0 ⇒ (UIncreasing(COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])), ≥)∧0 = 0∧[(-1)bni_70 + (-1)Bound*bni_70] + [(-1)bni_70]i69[10] ≥ 0∧0 = 0∧[(-1)bso_71] ≥ 0)

  • COND_LOAD12322(TRUE, i79, i85, i69) → LOAD1222(+(i79, -1), i85, i69)
    • (i69[10] ≥ 0∧i79[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧0 = 0∧[(-1)bni_72 + (-1)Bound*bni_72] + [(-1)bni_72]i69[10] ≥ 0∧0 = 0∧[(-1)bso_73] ≥ 0)

  • LOAD1222(i79, i85, i69) → COND_LOAD12223(&&(>=(i69, 0), >(i79, i69)), i79, i85, i69)
    • (i69[12] ≥ 0∧i79[12] ≥ 0 ⇒ (UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥)∧0 = 0∧[(-1)bni_74 + (-1)Bound*bni_74] + [(-1)bni_74]i69[12] ≥ 0∧0 = 0∧[(-1)bso_75] ≥ 0)

  • COND_LOAD12223(TRUE, i79, i85, i69) → LOAD1222(+(i79, -1), i85, i69)
    • (i69[12] ≥ 0∧i79[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧0 = 0∧[(-1)bni_76 + (-1)Bound*bni_76] + [(-1)bni_76]i69[12] ≥ 0∧0 = 0∧[(-1)bso_77] ≥ 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) = [1]   
POL(FALSE) = [3]   
POL(LOAD1222(x1, x2, x3)) = [-1] + [-1]x3   
POL(COND_LOAD1222(x1, x2, x3, x4)) = [-1] + [-1]x4   
POL(&&(x1, x2)) = [-1]   
POL(>=(x1, x2)) = [-1]   
POL(0) = 0   
POL(>(x1, x2)) = [-1]   
POL(<=(x1, x2)) = [-1]   
POL(LOAD1232(x1, x2, x3)) = [-1] + [-1]x3   
POL(COND_LOAD1232(x1, x2, x3, x4)) = [-1] + [-1]x4   
POL(COND_LOAD12221(x1, x2, x3, x4)) = [1] + [-1]x4 + x1   
POL(COND_LOAD12321(x1, x2, x3, x4)) = [-1] + [-1]x4   
POL(+(x1, x2)) = x1 + x2   
POL(-1) = [-1]   
POL(COND_LOAD12222(x1, x2, x3, x4)) = [-1] + [-1]x4 + [-1]x3 + [-1]x2 + [-1]x1   
POL(COND_LOAD12322(x1, x2, x3, x4)) = [-1] + [-1]x4   
POL(COND_LOAD12223(x1, x2, x3, x4)) = [-1] + [-1]x4   

The following pairs are in P>:

LOAD1222(i79[4], i85[4], i69[4]) → COND_LOAD12221(&&(&&(&&(<=(i85[4], i69[4]), <=(i79[4], i69[4])), >=(i69[4], 0)), >(i79[4], i69[4])), i79[4], i85[4], i69[4])
COND_LOAD12221(TRUE, i79[5], i85[5], i69[5]) → LOAD1222(i79[5], i85[5], i69[5])
LOAD1222(i79[8], i85[8], i69[8]) → COND_LOAD12222(&&(&&(&&(>=(i69[8], 0), >(i85[8], i69[8])), <=(i79[8], i69[8])), >(i79[8], i69[8])), i79[8], i85[8], i69[8])
COND_LOAD12222(TRUE, i79[9], i85[9], i69[9]) → LOAD1222(i79[9], +(i85[9], -1), i69[9])

The following pairs are in Pbound:

LOAD1222(i79[4], i85[4], i69[4]) → COND_LOAD12221(&&(&&(&&(<=(i85[4], i69[4]), <=(i79[4], i69[4])), >=(i69[4], 0)), >(i79[4], i69[4])), i79[4], i85[4], i69[4])
LOAD1222(i79[8], i85[8], i69[8]) → COND_LOAD12222(&&(&&(&&(>=(i69[8], 0), >(i85[8], i69[8])), <=(i79[8], i69[8])), >(i79[8], i69[8])), i79[8], i85[8], i69[8])
COND_LOAD12222(TRUE, i79[9], i85[9], i69[9]) → LOAD1222(i79[9], +(i85[9], -1), i69[9])

The following pairs are in P≥:

LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])
COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1])
LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])
COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3])
LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])
COND_LOAD12321(TRUE, i79[7], i85[7], i69[7]) → LOAD1222(i79[7], +(i85[7], -1), i69[7])
LOAD1232(i79[10], i85[10], i69[10]) → COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])
COND_LOAD12322(TRUE, i79[11], i85[11], i69[11]) → LOAD1222(+(i79[11], -1), i85[11], i69[11])
LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])
COND_LOAD12223(TRUE, i79[13], i85[13], i69[13]) → LOAD1222(+(i79[13], -1), i85[13], i69[13])

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

(10) Complex Obligation (AND)

(11) Obligation:

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


The following domains are used:

Boolean, Integer


R is empty.

The integer pair graph contains the following rules and edges:
(0): LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(i69[0] >= 0 && i85[0] > i69[0] && i79[0] <= i69[0], i79[0], i85[0], i69[0])
(1): COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1])
(2): LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(i85[2] <= i69[2] && i79[2] <= i69[2], i79[2], i85[2], i69[2])
(3): COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3])
(6): LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(i69[6] >= 0 && i85[6] > i69[6] && i79[6] <= i69[6], i79[6], i85[6], i69[6])
(7): COND_LOAD12321(TRUE, i79[7], i85[7], i69[7]) → LOAD1222(i79[7], i85[7] + -1, i69[7])
(10): LOAD1232(i79[10], i85[10], i69[10]) → COND_LOAD12322(i69[10] >= 0 && i79[10] > i69[10], i79[10], i85[10], i69[10])
(11): COND_LOAD12322(TRUE, i79[11], i85[11], i69[11]) → LOAD1222(i79[11] + -1, i85[11], i69[11])
(12): LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(i69[12] >= 0 && i79[12] > i69[12], i79[12], i85[12], i69[12])
(13): COND_LOAD12223(TRUE, i79[13], i85[13], i69[13]) → LOAD1222(i79[13] + -1, i85[13], i69[13])

(3) -> (0), if ((i79[3] →* i79[0])∧(i69[3] →* i69[0])∧(i85[3] →* i85[0]))


(7) -> (0), if ((i85[7] + -1 →* i85[0])∧(i79[7] →* i79[0])∧(i69[7] →* i69[0]))


(11) -> (0), if ((i79[11] + -1 →* i79[0])∧(i85[11] →* i85[0])∧(i69[11] →* i69[0]))


(13) -> (0), if ((i69[13] →* i69[0])∧(i79[13] + -1 →* i79[0])∧(i85[13] →* i85[0]))


(0) -> (1), if ((i79[0] →* i79[1])∧(i85[0] →* i85[1])∧(i69[0] →* i69[1])∧(i69[0] >= 0 && i85[0] > i69[0] && i79[0] <= i69[0] →* TRUE))


(1) -> (2), if ((i79[1] →* i79[2])∧(i69[1] →* i69[2])∧(i85[1] →* i85[2]))


(2) -> (3), if ((i85[2] →* i85[3])∧(i69[2] →* i69[3])∧(i85[2] <= i69[2] && i79[2] <= i69[2] →* TRUE)∧(i79[2] →* i79[3]))


(1) -> (6), if ((i79[1] →* i79[6])∧(i85[1] →* i85[6])∧(i69[1] →* i69[6]))


(6) -> (7), if ((i85[6] →* i85[7])∧(i69[6] >= 0 && i85[6] > i69[6] && i79[6] <= i69[6] →* TRUE)∧(i69[6] →* i69[7])∧(i79[6] →* i79[7]))


(1) -> (10), if ((i69[1] →* i69[10])∧(i79[1] →* i79[10])∧(i85[1] →* i85[10]))


(10) -> (11), if ((i85[10] →* i85[11])∧(i69[10] >= 0 && i79[10] > i69[10] →* TRUE)∧(i69[10] →* i69[11])∧(i79[10] →* i79[11]))


(3) -> (12), if ((i85[3] →* i85[12])∧(i69[3] →* i69[12])∧(i79[3] →* i79[12]))


(7) -> (12), if ((i79[7] →* i79[12])∧(i69[7] →* i69[12])∧(i85[7] + -1 →* i85[12]))


(11) -> (12), if ((i79[11] + -1 →* i79[12])∧(i85[11] →* i85[12])∧(i69[11] →* i69[12]))


(13) -> (12), if ((i69[13] →* i69[12])∧(i85[13] →* i85[12])∧(i79[13] + -1 →* i79[12]))


(12) -> (13), if ((i85[12] →* i85[13])∧(i69[12] →* i69[13])∧(i79[12] →* i79[13])∧(i69[12] >= 0 && i79[12] > i69[12] →* TRUE))



The set Q consists of the following terms:
Load1222(x0, x1, x2)
Cond_Load1222(TRUE, x0, x1, x2)
Load1232(x0, x1, x2)
Cond_Load1232(TRUE, x0, x1, x2)
Cond_Load12221(TRUE, x0, x1, x2)
Cond_Load12321(TRUE, x0, x1, x2)
Cond_Load12222(TRUE, x0, x1, x2)
Cond_Load12322(TRUE, x0, x1, x2)
Cond_Load12223(TRUE, x0, x1, x2)

(12) 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 LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]) the following chains were created:
  • We consider the chain LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]), COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1]) which results in the following constraint:

    (1)    (i79[0]=i79[1]∧i85[0]=i85[1]∧i69[0]=i69[1]∧&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0]))=TRUE ⇒ LOAD1222(i79[0], i85[0], i69[0])≥NonInfC∧LOAD1222(i79[0], i85[0], i69[0])≥COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])∧(UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥))



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

    (2)    (<=(i79[0], i69[0])=TRUE∧>=(i69[0], 0)=TRUE∧>(i85[0], i69[0])=TRUE ⇒ LOAD1222(i79[0], i85[0], i69[0])≥NonInfC∧LOAD1222(i79[0], i85[0], i69[0])≥COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])∧(UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥))



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

    (3)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] + [-1] + [-1]i69[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)bni_40 + (-1)Bound*bni_40] + [(-1)bni_40]i69[0] + [bni_40]i85[0] ≥ 0∧[(-1)bso_41] ≥ 0)



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

    (4)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] + [-1] + [-1]i69[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)bni_40 + (-1)Bound*bni_40] + [(-1)bni_40]i69[0] + [bni_40]i85[0] ≥ 0∧[(-1)bso_41] ≥ 0)



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

    (5)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] + [-1] + [-1]i69[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)bni_40 + (-1)Bound*bni_40] + [(-1)bni_40]i69[0] + [bni_40]i85[0] ≥ 0∧[(-1)bso_41] ≥ 0)



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

    (6)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_40] + [bni_40]i85[0] ≥ 0∧[(-1)bso_41] ≥ 0)



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

    (7)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_40] + [bni_40]i85[0] ≥ 0∧[(-1)bso_41] ≥ 0)


    (8)    (i69[0] + i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_40] + [bni_40]i85[0] ≥ 0∧[(-1)bso_41] ≥ 0)



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

    (9)    (i69[0] ≥ 0∧i79[0] + i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_40] + [bni_40]i85[0] ≥ 0∧[(-1)bso_41] ≥ 0)







For Pair COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1]) the following chains were created:
  • We consider the chain COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1]), LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2]) which results in the following constraint:

    (10)    (i79[1]=i79[2]∧i69[1]=i69[2]∧i85[1]=i85[2] ⇒ COND_LOAD1222(TRUE, i79[1], i85[1], i69[1])≥NonInfC∧COND_LOAD1222(TRUE, i79[1], i85[1], i69[1])≥LOAD1232(i79[1], i85[1], i69[1])∧(UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥))



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

    (11)    (COND_LOAD1222(TRUE, i79[1], i85[1], i69[1])≥NonInfC∧COND_LOAD1222(TRUE, i79[1], i85[1], i69[1])≥LOAD1232(i79[1], i85[1], i69[1])∧(UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥))



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

    (12)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_43] ≥ 0)



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

    (13)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_43] ≥ 0)



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

    (14)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_43] ≥ 0)



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

    (15)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_43] ≥ 0)



  • We consider the chain COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1]), LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6]) which results in the following constraint:

    (16)    (i79[1]=i79[6]∧i85[1]=i85[6]∧i69[1]=i69[6] ⇒ COND_LOAD1222(TRUE, i79[1], i85[1], i69[1])≥NonInfC∧COND_LOAD1222(TRUE, i79[1], i85[1], i69[1])≥LOAD1232(i79[1], i85[1], i69[1])∧(UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥))



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

    (17)    (COND_LOAD1222(TRUE, i79[1], i85[1], i69[1])≥NonInfC∧COND_LOAD1222(TRUE, i79[1], i85[1], i69[1])≥LOAD1232(i79[1], i85[1], i69[1])∧(UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥))



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

    (18)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_43] ≥ 0)



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

    (19)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_43] ≥ 0)



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

    (20)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_43] ≥ 0)



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

    (21)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_43] ≥ 0)



  • We consider the chain COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1]), LOAD1232(i79[10], i85[10], i69[10]) → COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10]) which results in the following constraint:

    (22)    (i69[1]=i69[10]∧i79[1]=i79[10]∧i85[1]=i85[10] ⇒ COND_LOAD1222(TRUE, i79[1], i85[1], i69[1])≥NonInfC∧COND_LOAD1222(TRUE, i79[1], i85[1], i69[1])≥LOAD1232(i79[1], i85[1], i69[1])∧(UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥))



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

    (23)    (COND_LOAD1222(TRUE, i79[1], i85[1], i69[1])≥NonInfC∧COND_LOAD1222(TRUE, i79[1], i85[1], i69[1])≥LOAD1232(i79[1], i85[1], i69[1])∧(UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥))



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

    (24)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_43] ≥ 0)



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

    (25)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_43] ≥ 0)



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

    (26)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_43] ≥ 0)



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

    (27)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_43] ≥ 0)







For Pair LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2]) the following chains were created:
  • We consider the chain LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2]), COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3]) which results in the following constraint:

    (28)    (i85[2]=i85[3]∧i69[2]=i69[3]∧&&(<=(i85[2], i69[2]), <=(i79[2], i69[2]))=TRUE∧i79[2]=i79[3] ⇒ LOAD1232(i79[2], i85[2], i69[2])≥NonInfC∧LOAD1232(i79[2], i85[2], i69[2])≥COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])∧(UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥))



    We simplified constraint (28) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (29)    (<=(i85[2], i69[2])=TRUE∧<=(i79[2], i69[2])=TRUE ⇒ LOAD1232(i79[2], i85[2], i69[2])≥NonInfC∧LOAD1232(i79[2], i85[2], i69[2])≥COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])∧(UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥))



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

    (30)    (i69[2] + [-1]i85[2] ≥ 0∧i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_44 + (-1)Bound*bni_44] + [(-1)bni_44]i69[2] + [bni_44]i85[2] ≥ 0∧[(-1)bso_45] ≥ 0)



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

    (31)    (i69[2] + [-1]i85[2] ≥ 0∧i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_44 + (-1)Bound*bni_44] + [(-1)bni_44]i69[2] + [bni_44]i85[2] ≥ 0∧[(-1)bso_45] ≥ 0)



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

    (32)    (i69[2] + [-1]i85[2] ≥ 0∧i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_44 + (-1)Bound*bni_44] + [(-1)bni_44]i69[2] + [bni_44]i85[2] ≥ 0∧[(-1)bso_45] ≥ 0)



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

    (33)    (i69[2] ≥ 0∧i85[2] + i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_44 + (-1)Bound*bni_44] + [(-1)bni_44]i69[2] ≥ 0∧[(-1)bso_45] ≥ 0)



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

    (34)    (i69[2] ≥ 0∧i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_44 + (-1)Bound*bni_44] + [(-1)bni_44]i69[2] ≥ 0∧[(-1)bso_45] ≥ 0)



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

    (35)    (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_44 + (-1)Bound*bni_44] + [(-1)bni_44]i69[2] ≥ 0∧[(-1)bso_45] ≥ 0)


    (36)    (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_44 + (-1)Bound*bni_44] + [(-1)bni_44]i69[2] ≥ 0∧[(-1)bso_45] ≥ 0)







For Pair COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3]) the following chains were created:
  • We consider the chain COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3]), LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]) which results in the following constraint:

    (37)    (i79[3]=i79[0]∧i69[3]=i69[0]∧i85[3]=i85[0] ⇒ COND_LOAD1232(TRUE, i79[3], i85[3], i69[3])≥NonInfC∧COND_LOAD1232(TRUE, i79[3], i85[3], i69[3])≥LOAD1222(i79[3], i85[3], i69[3])∧(UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥))



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

    (38)    (COND_LOAD1232(TRUE, i79[3], i85[3], i69[3])≥NonInfC∧COND_LOAD1232(TRUE, i79[3], i85[3], i69[3])≥LOAD1222(i79[3], i85[3], i69[3])∧(UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥))



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

    (39)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bso_47] ≥ 0)



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

    (40)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bso_47] ≥ 0)



    We simplified constraint (40) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (41)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bso_47] ≥ 0)



    We simplified constraint (41) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

    (42)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_47] ≥ 0)



  • We consider the chain COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3]), LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12]) which results in the following constraint:

    (43)    (i85[3]=i85[12]∧i69[3]=i69[12]∧i79[3]=i79[12] ⇒ COND_LOAD1232(TRUE, i79[3], i85[3], i69[3])≥NonInfC∧COND_LOAD1232(TRUE, i79[3], i85[3], i69[3])≥LOAD1222(i79[3], i85[3], i69[3])∧(UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥))



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

    (44)    (COND_LOAD1232(TRUE, i79[3], i85[3], i69[3])≥NonInfC∧COND_LOAD1232(TRUE, i79[3], i85[3], i69[3])≥LOAD1222(i79[3], i85[3], i69[3])∧(UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥))



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

    (45)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bso_47] ≥ 0)



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

    (46)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bso_47] ≥ 0)



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

    (47)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bso_47] ≥ 0)



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

    (48)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_47] ≥ 0)







For Pair LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6]) the following chains were created:
  • We consider the chain LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6]), COND_LOAD12321(TRUE, i79[7], i85[7], i69[7]) → LOAD1222(i79[7], +(i85[7], -1), i69[7]) which results in the following constraint:

    (49)    (i85[6]=i85[7]∧&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6]))=TRUE∧i69[6]=i69[7]∧i79[6]=i79[7] ⇒ LOAD1232(i79[6], i85[6], i69[6])≥NonInfC∧LOAD1232(i79[6], i85[6], i69[6])≥COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])∧(UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥))



    We simplified constraint (49) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (50)    (<=(i79[6], i69[6])=TRUE∧>=(i69[6], 0)=TRUE∧>(i85[6], i69[6])=TRUE ⇒ LOAD1232(i79[6], i85[6], i69[6])≥NonInfC∧LOAD1232(i79[6], i85[6], i69[6])≥COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])∧(UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥))



    We simplified constraint (50) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (51)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] + [-1] + [-1]i69[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)bni_48 + (-1)Bound*bni_48] + [(-1)bni_48]i69[6] + [bni_48]i85[6] ≥ 0∧[(-1)bso_49] ≥ 0)



    We simplified constraint (51) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (52)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] + [-1] + [-1]i69[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)bni_48 + (-1)Bound*bni_48] + [(-1)bni_48]i69[6] + [bni_48]i85[6] ≥ 0∧[(-1)bso_49] ≥ 0)



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

    (53)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] + [-1] + [-1]i69[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)bni_48 + (-1)Bound*bni_48] + [(-1)bni_48]i69[6] + [bni_48]i85[6] ≥ 0∧[(-1)bso_49] ≥ 0)



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

    (54)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)Bound*bni_48] + [bni_48]i85[6] ≥ 0∧[(-1)bso_49] ≥ 0)



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

    (55)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)Bound*bni_48] + [bni_48]i85[6] ≥ 0∧[(-1)bso_49] ≥ 0)


    (56)    (i69[6] + i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)Bound*bni_48] + [bni_48]i85[6] ≥ 0∧[(-1)bso_49] ≥ 0)



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

    (57)    (i69[6] ≥ 0∧i79[6] + i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)Bound*bni_48] + [bni_48]i85[6] ≥ 0∧[(-1)bso_49] ≥ 0)







For Pair COND_LOAD12321(TRUE, i79[7], i85[7], i69[7]) → LOAD1222(i79[7], +(i85[7], -1), i69[7]) the following chains were created:
  • We consider the chain LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6]), COND_LOAD12321(TRUE, i79[7], i85[7], i69[7]) → LOAD1222(i79[7], +(i85[7], -1), i69[7]), LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]) which results in the following constraint:

    (58)    (i85[6]=i85[7]∧&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6]))=TRUE∧i69[6]=i69[7]∧i79[6]=i79[7]∧+(i85[7], -1)=i85[0]∧i79[7]=i79[0]∧i69[7]=i69[0] ⇒ COND_LOAD12321(TRUE, i79[7], i85[7], i69[7])≥NonInfC∧COND_LOAD12321(TRUE, i79[7], i85[7], i69[7])≥LOAD1222(i79[7], +(i85[7], -1), i69[7])∧(UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥))



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

    (59)    (<=(i79[6], i69[6])=TRUE∧>=(i69[6], 0)=TRUE∧>(i85[6], i69[6])=TRUE ⇒ COND_LOAD12321(TRUE, i79[6], i85[6], i69[6])≥NonInfC∧COND_LOAD12321(TRUE, i79[6], i85[6], i69[6])≥LOAD1222(i79[6], +(i85[6], -1), i69[6])∧(UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥))



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

    (60)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] + [-1] + [-1]i69[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)bni_50 + (-1)Bound*bni_50] + [(-1)bni_50]i69[6] + [bni_50]i85[6] ≥ 0∧[1 + (-1)bso_51] ≥ 0)



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

    (61)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] + [-1] + [-1]i69[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)bni_50 + (-1)Bound*bni_50] + [(-1)bni_50]i69[6] + [bni_50]i85[6] ≥ 0∧[1 + (-1)bso_51] ≥ 0)



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

    (62)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] + [-1] + [-1]i69[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)bni_50 + (-1)Bound*bni_50] + [(-1)bni_50]i69[6] + [bni_50]i85[6] ≥ 0∧[1 + (-1)bso_51] ≥ 0)



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

    (63)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_50] + [bni_50]i85[6] ≥ 0∧[1 + (-1)bso_51] ≥ 0)



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

    (64)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_50] + [bni_50]i85[6] ≥ 0∧[1 + (-1)bso_51] ≥ 0)


    (65)    (i69[6] + i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_50] + [bni_50]i85[6] ≥ 0∧[1 + (-1)bso_51] ≥ 0)



    We simplified constraint (64) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (66)    (i69[6] ≥ 0∧i79[6] + i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_50] + [bni_50]i85[6] ≥ 0∧[1 + (-1)bso_51] ≥ 0)



  • We consider the chain LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6]), COND_LOAD12321(TRUE, i79[7], i85[7], i69[7]) → LOAD1222(i79[7], +(i85[7], -1), i69[7]), LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12]) which results in the following constraint:

    (67)    (i85[6]=i85[7]∧&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6]))=TRUE∧i69[6]=i69[7]∧i79[6]=i79[7]∧i79[7]=i79[12]∧i69[7]=i69[12]∧+(i85[7], -1)=i85[12] ⇒ COND_LOAD12321(TRUE, i79[7], i85[7], i69[7])≥NonInfC∧COND_LOAD12321(TRUE, i79[7], i85[7], i69[7])≥LOAD1222(i79[7], +(i85[7], -1), i69[7])∧(UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥))



    We simplified constraint (67) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (68)    (<=(i79[6], i69[6])=TRUE∧>=(i69[6], 0)=TRUE∧>(i85[6], i69[6])=TRUE ⇒ COND_LOAD12321(TRUE, i79[6], i85[6], i69[6])≥NonInfC∧COND_LOAD12321(TRUE, i79[6], i85[6], i69[6])≥LOAD1222(i79[6], +(i85[6], -1), i69[6])∧(UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥))



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

    (69)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] + [-1] + [-1]i69[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)bni_50 + (-1)Bound*bni_50] + [(-1)bni_50]i69[6] + [bni_50]i85[6] ≥ 0∧[1 + (-1)bso_51] ≥ 0)



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

    (70)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] + [-1] + [-1]i69[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)bni_50 + (-1)Bound*bni_50] + [(-1)bni_50]i69[6] + [bni_50]i85[6] ≥ 0∧[1 + (-1)bso_51] ≥ 0)



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

    (71)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] + [-1] + [-1]i69[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)bni_50 + (-1)Bound*bni_50] + [(-1)bni_50]i69[6] + [bni_50]i85[6] ≥ 0∧[1 + (-1)bso_51] ≥ 0)



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

    (72)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_50] + [bni_50]i85[6] ≥ 0∧[1 + (-1)bso_51] ≥ 0)



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

    (73)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_50] + [bni_50]i85[6] ≥ 0∧[1 + (-1)bso_51] ≥ 0)


    (74)    (i69[6] + i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_50] + [bni_50]i85[6] ≥ 0∧[1 + (-1)bso_51] ≥ 0)



    We simplified constraint (73) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (75)    (i69[6] ≥ 0∧i79[6] + i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_50] + [bni_50]i85[6] ≥ 0∧[1 + (-1)bso_51] ≥ 0)







For Pair LOAD1232(i79[10], i85[10], i69[10]) → COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10]) the following chains were created:
  • We consider the chain LOAD1232(i79[10], i85[10], i69[10]) → COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10]), COND_LOAD12322(TRUE, i79[11], i85[11], i69[11]) → LOAD1222(+(i79[11], -1), i85[11], i69[11]) which results in the following constraint:

    (76)    (i85[10]=i85[11]∧&&(>=(i69[10], 0), >(i79[10], i69[10]))=TRUE∧i69[10]=i69[11]∧i79[10]=i79[11] ⇒ LOAD1232(i79[10], i85[10], i69[10])≥NonInfC∧LOAD1232(i79[10], i85[10], i69[10])≥COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])∧(UIncreasing(COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])), ≥))



    We simplified constraint (76) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (77)    (>=(i69[10], 0)=TRUE∧>(i79[10], i69[10])=TRUE ⇒ LOAD1232(i79[10], i85[10], i69[10])≥NonInfC∧LOAD1232(i79[10], i85[10], i69[10])≥COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])∧(UIncreasing(COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])), ≥))



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

    (78)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])), ≥)∧[(-1)bni_52 + (-1)Bound*bni_52] + [(-1)bni_52]i69[10] + [bni_52]i85[10] ≥ 0∧[(-1)bso_53] ≥ 0)



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

    (79)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])), ≥)∧[(-1)bni_52 + (-1)Bound*bni_52] + [(-1)bni_52]i69[10] + [bni_52]i85[10] ≥ 0∧[(-1)bso_53] ≥ 0)



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

    (80)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])), ≥)∧[(-1)bni_52 + (-1)Bound*bni_52] + [(-1)bni_52]i69[10] + [bni_52]i85[10] ≥ 0∧[(-1)bso_53] ≥ 0)



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

    (81)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])), ≥)∧[bni_52] = 0∧[(-1)bni_52 + (-1)Bound*bni_52] + [(-1)bni_52]i69[10] ≥ 0∧0 = 0∧[(-1)bso_53] ≥ 0)



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

    (82)    (i69[10] ≥ 0∧i79[10] ≥ 0 ⇒ (UIncreasing(COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])), ≥)∧[bni_52] = 0∧[(-1)bni_52 + (-1)Bound*bni_52] + [(-1)bni_52]i69[10] ≥ 0∧0 = 0∧[(-1)bso_53] ≥ 0)







For Pair COND_LOAD12322(TRUE, i79[11], i85[11], i69[11]) → LOAD1222(+(i79[11], -1), i85[11], i69[11]) the following chains were created:
  • We consider the chain LOAD1232(i79[10], i85[10], i69[10]) → COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10]), COND_LOAD12322(TRUE, i79[11], i85[11], i69[11]) → LOAD1222(+(i79[11], -1), i85[11], i69[11]), LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]) which results in the following constraint:

    (83)    (i85[10]=i85[11]∧&&(>=(i69[10], 0), >(i79[10], i69[10]))=TRUE∧i69[10]=i69[11]∧i79[10]=i79[11]∧+(i79[11], -1)=i79[0]∧i85[11]=i85[0]∧i69[11]=i69[0] ⇒ COND_LOAD12322(TRUE, i79[11], i85[11], i69[11])≥NonInfC∧COND_LOAD12322(TRUE, i79[11], i85[11], i69[11])≥LOAD1222(+(i79[11], -1), i85[11], i69[11])∧(UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥))



    We simplified constraint (83) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (84)    (>=(i69[10], 0)=TRUE∧>(i79[10], i69[10])=TRUE ⇒ COND_LOAD12322(TRUE, i79[10], i85[10], i69[10])≥NonInfC∧COND_LOAD12322(TRUE, i79[10], i85[10], i69[10])≥LOAD1222(+(i79[10], -1), i85[10], i69[10])∧(UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥))



    We simplified constraint (84) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (85)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧[(-1)bni_54 + (-1)Bound*bni_54] + [(-1)bni_54]i69[10] + [bni_54]i85[10] ≥ 0∧[(-1)bso_55] ≥ 0)



    We simplified constraint (85) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (86)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧[(-1)bni_54 + (-1)Bound*bni_54] + [(-1)bni_54]i69[10] + [bni_54]i85[10] ≥ 0∧[(-1)bso_55] ≥ 0)



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

    (87)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧[(-1)bni_54 + (-1)Bound*bni_54] + [(-1)bni_54]i69[10] + [bni_54]i85[10] ≥ 0∧[(-1)bso_55] ≥ 0)



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

    (88)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧[bni_54] = 0∧[(-1)bni_54 + (-1)Bound*bni_54] + [(-1)bni_54]i69[10] ≥ 0∧0 = 0∧[(-1)bso_55] ≥ 0)



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

    (89)    (i69[10] ≥ 0∧i79[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧[bni_54] = 0∧[(-1)bni_54 + (-1)Bound*bni_54] + [(-1)bni_54]i69[10] ≥ 0∧0 = 0∧[(-1)bso_55] ≥ 0)



  • We consider the chain LOAD1232(i79[10], i85[10], i69[10]) → COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10]), COND_LOAD12322(TRUE, i79[11], i85[11], i69[11]) → LOAD1222(+(i79[11], -1), i85[11], i69[11]), LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12]) which results in the following constraint:

    (90)    (i85[10]=i85[11]∧&&(>=(i69[10], 0), >(i79[10], i69[10]))=TRUE∧i69[10]=i69[11]∧i79[10]=i79[11]∧+(i79[11], -1)=i79[12]∧i85[11]=i85[12]∧i69[11]=i69[12] ⇒ COND_LOAD12322(TRUE, i79[11], i85[11], i69[11])≥NonInfC∧COND_LOAD12322(TRUE, i79[11], i85[11], i69[11])≥LOAD1222(+(i79[11], -1), i85[11], i69[11])∧(UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥))



    We simplified constraint (90) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (91)    (>=(i69[10], 0)=TRUE∧>(i79[10], i69[10])=TRUE ⇒ COND_LOAD12322(TRUE, i79[10], i85[10], i69[10])≥NonInfC∧COND_LOAD12322(TRUE, i79[10], i85[10], i69[10])≥LOAD1222(+(i79[10], -1), i85[10], i69[10])∧(UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥))



    We simplified constraint (91) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (92)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧[(-1)bni_54 + (-1)Bound*bni_54] + [(-1)bni_54]i69[10] + [bni_54]i85[10] ≥ 0∧[(-1)bso_55] ≥ 0)



    We simplified constraint (92) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (93)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧[(-1)bni_54 + (-1)Bound*bni_54] + [(-1)bni_54]i69[10] + [bni_54]i85[10] ≥ 0∧[(-1)bso_55] ≥ 0)



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

    (94)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧[(-1)bni_54 + (-1)Bound*bni_54] + [(-1)bni_54]i69[10] + [bni_54]i85[10] ≥ 0∧[(-1)bso_55] ≥ 0)



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

    (95)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧[bni_54] = 0∧[(-1)bni_54 + (-1)Bound*bni_54] + [(-1)bni_54]i69[10] ≥ 0∧0 = 0∧[(-1)bso_55] ≥ 0)



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

    (96)    (i69[10] ≥ 0∧i79[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧[bni_54] = 0∧[(-1)bni_54 + (-1)Bound*bni_54] + [(-1)bni_54]i69[10] ≥ 0∧0 = 0∧[(-1)bso_55] ≥ 0)







For Pair LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12]) the following chains were created:
  • We consider the chain LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12]), COND_LOAD12223(TRUE, i79[13], i85[13], i69[13]) → LOAD1222(+(i79[13], -1), i85[13], i69[13]) which results in the following constraint:

    (97)    (i85[12]=i85[13]∧i69[12]=i69[13]∧i79[12]=i79[13]∧&&(>=(i69[12], 0), >(i79[12], i69[12]))=TRUE ⇒ LOAD1222(i79[12], i85[12], i69[12])≥NonInfC∧LOAD1222(i79[12], i85[12], i69[12])≥COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])∧(UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥))



    We simplified constraint (97) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (98)    (>=(i69[12], 0)=TRUE∧>(i79[12], i69[12])=TRUE ⇒ LOAD1222(i79[12], i85[12], i69[12])≥NonInfC∧LOAD1222(i79[12], i85[12], i69[12])≥COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])∧(UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥))



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

    (99)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥)∧[(-1)bni_56 + (-1)Bound*bni_56] + [(-1)bni_56]i69[12] + [bni_56]i85[12] ≥ 0∧[(-1)bso_57] ≥ 0)



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

    (100)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥)∧[(-1)bni_56 + (-1)Bound*bni_56] + [(-1)bni_56]i69[12] + [bni_56]i85[12] ≥ 0∧[(-1)bso_57] ≥ 0)



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

    (101)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥)∧[(-1)bni_56 + (-1)Bound*bni_56] + [(-1)bni_56]i69[12] + [bni_56]i85[12] ≥ 0∧[(-1)bso_57] ≥ 0)



    We simplified constraint (101) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

    (102)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥)∧[bni_56] = 0∧[(-1)bni_56 + (-1)Bound*bni_56] + [(-1)bni_56]i69[12] ≥ 0∧0 = 0∧[(-1)bso_57] ≥ 0)



    We simplified constraint (102) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (103)    (i69[12] ≥ 0∧i79[12] ≥ 0 ⇒ (UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥)∧[bni_56] = 0∧[(-1)bni_56 + (-1)Bound*bni_56] + [(-1)bni_56]i69[12] ≥ 0∧0 = 0∧[(-1)bso_57] ≥ 0)







For Pair COND_LOAD12223(TRUE, i79[13], i85[13], i69[13]) → LOAD1222(+(i79[13], -1), i85[13], i69[13]) the following chains were created:
  • We consider the chain LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12]), COND_LOAD12223(TRUE, i79[13], i85[13], i69[13]) → LOAD1222(+(i79[13], -1), i85[13], i69[13]), LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]) which results in the following constraint:

    (104)    (i85[12]=i85[13]∧i69[12]=i69[13]∧i79[12]=i79[13]∧&&(>=(i69[12], 0), >(i79[12], i69[12]))=TRUE∧i69[13]=i69[0]∧+(i79[13], -1)=i79[0]∧i85[13]=i85[0] ⇒ COND_LOAD12223(TRUE, i79[13], i85[13], i69[13])≥NonInfC∧COND_LOAD12223(TRUE, i79[13], i85[13], i69[13])≥LOAD1222(+(i79[13], -1), i85[13], i69[13])∧(UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥))



    We simplified constraint (104) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (105)    (>=(i69[12], 0)=TRUE∧>(i79[12], i69[12])=TRUE ⇒ COND_LOAD12223(TRUE, i79[12], i85[12], i69[12])≥NonInfC∧COND_LOAD12223(TRUE, i79[12], i85[12], i69[12])≥LOAD1222(+(i79[12], -1), i85[12], i69[12])∧(UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥))



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

    (106)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧[(-1)bni_58 + (-1)Bound*bni_58] + [(-1)bni_58]i69[12] + [bni_58]i85[12] ≥ 0∧[(-1)bso_59] ≥ 0)



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

    (107)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧[(-1)bni_58 + (-1)Bound*bni_58] + [(-1)bni_58]i69[12] + [bni_58]i85[12] ≥ 0∧[(-1)bso_59] ≥ 0)



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

    (108)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧[(-1)bni_58 + (-1)Bound*bni_58] + [(-1)bni_58]i69[12] + [bni_58]i85[12] ≥ 0∧[(-1)bso_59] ≥ 0)



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

    (109)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧[bni_58] = 0∧[(-1)bni_58 + (-1)Bound*bni_58] + [(-1)bni_58]i69[12] ≥ 0∧0 = 0∧[(-1)bso_59] ≥ 0)



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

    (110)    (i69[12] ≥ 0∧i79[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧[bni_58] = 0∧[(-1)bni_58 + (-1)Bound*bni_58] + [(-1)bni_58]i69[12] ≥ 0∧0 = 0∧[(-1)bso_59] ≥ 0)



  • We consider the chain LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12]), COND_LOAD12223(TRUE, i79[13], i85[13], i69[13]) → LOAD1222(+(i79[13], -1), i85[13], i69[13]), LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12]) which results in the following constraint:

    (111)    (i85[12]=i85[13]∧i69[12]=i69[13]∧i79[12]=i79[13]∧&&(>=(i69[12], 0), >(i79[12], i69[12]))=TRUE∧i69[13]=i69[12]1∧i85[13]=i85[12]1∧+(i79[13], -1)=i79[12]1 ⇒ COND_LOAD12223(TRUE, i79[13], i85[13], i69[13])≥NonInfC∧COND_LOAD12223(TRUE, i79[13], i85[13], i69[13])≥LOAD1222(+(i79[13], -1), i85[13], i69[13])∧(UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥))



    We simplified constraint (111) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (112)    (>=(i69[12], 0)=TRUE∧>(i79[12], i69[12])=TRUE ⇒ COND_LOAD12223(TRUE, i79[12], i85[12], i69[12])≥NonInfC∧COND_LOAD12223(TRUE, i79[12], i85[12], i69[12])≥LOAD1222(+(i79[12], -1), i85[12], i69[12])∧(UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥))



    We simplified constraint (112) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (113)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧[(-1)bni_58 + (-1)Bound*bni_58] + [(-1)bni_58]i69[12] + [bni_58]i85[12] ≥ 0∧[(-1)bso_59] ≥ 0)



    We simplified constraint (113) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (114)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧[(-1)bni_58 + (-1)Bound*bni_58] + [(-1)bni_58]i69[12] + [bni_58]i85[12] ≥ 0∧[(-1)bso_59] ≥ 0)



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

    (115)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧[(-1)bni_58 + (-1)Bound*bni_58] + [(-1)bni_58]i69[12] + [bni_58]i85[12] ≥ 0∧[(-1)bso_59] ≥ 0)



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

    (116)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧[bni_58] = 0∧[(-1)bni_58 + (-1)Bound*bni_58] + [(-1)bni_58]i69[12] ≥ 0∧0 = 0∧[(-1)bso_59] ≥ 0)



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

    (117)    (i69[12] ≥ 0∧i79[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧[bni_58] = 0∧[(-1)bni_58 + (-1)Bound*bni_58] + [(-1)bni_58]i69[12] ≥ 0∧0 = 0∧[(-1)bso_59] ≥ 0)







To summarize, we get the following constraints P≥ for the following pairs.
  • LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])
    • (i69[0] + i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_40] + [bni_40]i85[0] ≥ 0∧[(-1)bso_41] ≥ 0)
    • (i69[0] ≥ 0∧i79[0] + i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_40] + [bni_40]i85[0] ≥ 0∧[(-1)bso_41] ≥ 0)

  • COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1])
    • ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_43] ≥ 0)
    • ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_43] ≥ 0)
    • ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_43] ≥ 0)

  • LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])
    • (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_44 + (-1)Bound*bni_44] + [(-1)bni_44]i69[2] ≥ 0∧[(-1)bso_45] ≥ 0)
    • (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_44 + (-1)Bound*bni_44] + [(-1)bni_44]i69[2] ≥ 0∧[(-1)bso_45] ≥ 0)

  • COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3])
    • ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_47] ≥ 0)
    • ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_47] ≥ 0)

  • LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])
    • (i69[6] + i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)Bound*bni_48] + [bni_48]i85[6] ≥ 0∧[(-1)bso_49] ≥ 0)
    • (i69[6] ≥ 0∧i79[6] + i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)Bound*bni_48] + [bni_48]i85[6] ≥ 0∧[(-1)bso_49] ≥ 0)

  • COND_LOAD12321(TRUE, i79[7], i85[7], i69[7]) → LOAD1222(i79[7], +(i85[7], -1), i69[7])
    • (i69[6] + i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_50] + [bni_50]i85[6] ≥ 0∧[1 + (-1)bso_51] ≥ 0)
    • (i69[6] ≥ 0∧i79[6] + i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_50] + [bni_50]i85[6] ≥ 0∧[1 + (-1)bso_51] ≥ 0)
    • (i69[6] + i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_50] + [bni_50]i85[6] ≥ 0∧[1 + (-1)bso_51] ≥ 0)
    • (i69[6] ≥ 0∧i79[6] + i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_50] + [bni_50]i85[6] ≥ 0∧[1 + (-1)bso_51] ≥ 0)

  • LOAD1232(i79[10], i85[10], i69[10]) → COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])
    • (i69[10] ≥ 0∧i79[10] ≥ 0 ⇒ (UIncreasing(COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])), ≥)∧[bni_52] = 0∧[(-1)bni_52 + (-1)Bound*bni_52] + [(-1)bni_52]i69[10] ≥ 0∧0 = 0∧[(-1)bso_53] ≥ 0)

  • COND_LOAD12322(TRUE, i79[11], i85[11], i69[11]) → LOAD1222(+(i79[11], -1), i85[11], i69[11])
    • (i69[10] ≥ 0∧i79[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧[bni_54] = 0∧[(-1)bni_54 + (-1)Bound*bni_54] + [(-1)bni_54]i69[10] ≥ 0∧0 = 0∧[(-1)bso_55] ≥ 0)
    • (i69[10] ≥ 0∧i79[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧[bni_54] = 0∧[(-1)bni_54 + (-1)Bound*bni_54] + [(-1)bni_54]i69[10] ≥ 0∧0 = 0∧[(-1)bso_55] ≥ 0)

  • LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])
    • (i69[12] ≥ 0∧i79[12] ≥ 0 ⇒ (UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥)∧[bni_56] = 0∧[(-1)bni_56 + (-1)Bound*bni_56] + [(-1)bni_56]i69[12] ≥ 0∧0 = 0∧[(-1)bso_57] ≥ 0)

  • COND_LOAD12223(TRUE, i79[13], i85[13], i69[13]) → LOAD1222(+(i79[13], -1), i85[13], i69[13])
    • (i69[12] ≥ 0∧i79[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧[bni_58] = 0∧[(-1)bni_58 + (-1)Bound*bni_58] + [(-1)bni_58]i69[12] ≥ 0∧0 = 0∧[(-1)bso_59] ≥ 0)
    • (i69[12] ≥ 0∧i79[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧[bni_58] = 0∧[(-1)bni_58 + (-1)Bound*bni_58] + [(-1)bni_58]i69[12] ≥ 0∧0 = 0∧[(-1)bso_59] ≥ 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) = [1]   
POL(LOAD1222(x1, x2, x3)) = [-1] + [-1]x3 + x2   
POL(COND_LOAD1222(x1, x2, x3, x4)) = [-1] + [-1]x4 + x3   
POL(&&(x1, x2)) = [-1]   
POL(>=(x1, x2)) = [-1]   
POL(0) = 0   
POL(>(x1, x2)) = [-1]   
POL(<=(x1, x2)) = [-1]   
POL(LOAD1232(x1, x2, x3)) = [-1] + [-1]x3 + x2   
POL(COND_LOAD1232(x1, x2, x3, x4)) = [-1] + [-1]x4 + x3   
POL(COND_LOAD12321(x1, x2, x3, x4)) = [-1] + [-1]x4 + x3   
POL(+(x1, x2)) = x1 + x2   
POL(-1) = [-1]   
POL(COND_LOAD12322(x1, x2, x3, x4)) = [-1] + [-1]x4 + x3   
POL(COND_LOAD12223(x1, x2, x3, x4)) = [-1] + [-1]x4 + x3   

The following pairs are in P>:

COND_LOAD12321(TRUE, i79[7], i85[7], i69[7]) → LOAD1222(i79[7], +(i85[7], -1), i69[7])

The following pairs are in Pbound:

LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])
LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])
COND_LOAD12321(TRUE, i79[7], i85[7], i69[7]) → LOAD1222(i79[7], +(i85[7], -1), i69[7])

The following pairs are in P≥:

LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])
COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1])
LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])
COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3])
LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])
LOAD1232(i79[10], i85[10], i69[10]) → COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])
COND_LOAD12322(TRUE, i79[11], i85[11], i69[11]) → LOAD1222(+(i79[11], -1), i85[11], i69[11])
LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])
COND_LOAD12223(TRUE, i79[13], i85[13], i69[13]) → LOAD1222(+(i79[13], -1), i85[13], i69[13])

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

(13) Complex Obligation (AND)

(14) Obligation:

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


The following domains are used:

Boolean, Integer


R is empty.

The integer pair graph contains the following rules and edges:
(0): LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(i69[0] >= 0 && i85[0] > i69[0] && i79[0] <= i69[0], i79[0], i85[0], i69[0])
(1): COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1])
(2): LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(i85[2] <= i69[2] && i79[2] <= i69[2], i79[2], i85[2], i69[2])
(3): COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3])
(6): LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(i69[6] >= 0 && i85[6] > i69[6] && i79[6] <= i69[6], i79[6], i85[6], i69[6])
(10): LOAD1232(i79[10], i85[10], i69[10]) → COND_LOAD12322(i69[10] >= 0 && i79[10] > i69[10], i79[10], i85[10], i69[10])
(11): COND_LOAD12322(TRUE, i79[11], i85[11], i69[11]) → LOAD1222(i79[11] + -1, i85[11], i69[11])
(12): LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(i69[12] >= 0 && i79[12] > i69[12], i79[12], i85[12], i69[12])
(13): COND_LOAD12223(TRUE, i79[13], i85[13], i69[13]) → LOAD1222(i79[13] + -1, i85[13], i69[13])

(3) -> (0), if ((i79[3] →* i79[0])∧(i69[3] →* i69[0])∧(i85[3] →* i85[0]))


(11) -> (0), if ((i79[11] + -1 →* i79[0])∧(i85[11] →* i85[0])∧(i69[11] →* i69[0]))


(13) -> (0), if ((i69[13] →* i69[0])∧(i79[13] + -1 →* i79[0])∧(i85[13] →* i85[0]))


(0) -> (1), if ((i79[0] →* i79[1])∧(i85[0] →* i85[1])∧(i69[0] →* i69[1])∧(i69[0] >= 0 && i85[0] > i69[0] && i79[0] <= i69[0] →* TRUE))


(1) -> (2), if ((i79[1] →* i79[2])∧(i69[1] →* i69[2])∧(i85[1] →* i85[2]))


(2) -> (3), if ((i85[2] →* i85[3])∧(i69[2] →* i69[3])∧(i85[2] <= i69[2] && i79[2] <= i69[2] →* TRUE)∧(i79[2] →* i79[3]))


(1) -> (6), if ((i79[1] →* i79[6])∧(i85[1] →* i85[6])∧(i69[1] →* i69[6]))


(1) -> (10), if ((i69[1] →* i69[10])∧(i79[1] →* i79[10])∧(i85[1] →* i85[10]))


(10) -> (11), if ((i85[10] →* i85[11])∧(i69[10] >= 0 && i79[10] > i69[10] →* TRUE)∧(i69[10] →* i69[11])∧(i79[10] →* i79[11]))


(3) -> (12), if ((i85[3] →* i85[12])∧(i69[3] →* i69[12])∧(i79[3] →* i79[12]))


(11) -> (12), if ((i79[11] + -1 →* i79[12])∧(i85[11] →* i85[12])∧(i69[11] →* i69[12]))


(13) -> (12), if ((i69[13] →* i69[12])∧(i85[13] →* i85[12])∧(i79[13] + -1 →* i79[12]))


(12) -> (13), if ((i85[12] →* i85[13])∧(i69[12] →* i69[13])∧(i79[12] →* i79[13])∧(i69[12] >= 0 && i79[12] > i69[12] →* TRUE))



The set Q consists of the following terms:
Load1222(x0, x1, x2)
Cond_Load1222(TRUE, x0, x1, x2)
Load1232(x0, x1, x2)
Cond_Load1232(TRUE, x0, x1, x2)
Cond_Load12221(TRUE, x0, x1, x2)
Cond_Load12321(TRUE, x0, x1, x2)
Cond_Load12222(TRUE, x0, x1, x2)
Cond_Load12322(TRUE, x0, x1, x2)
Cond_Load12223(TRUE, x0, x1, x2)

(15) IDependencyGraphProof (EQUIVALENT transformation)

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

(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:

Integer, Boolean


R is empty.

The integer pair graph contains the following rules and edges:
(11): COND_LOAD12322(TRUE, i79[11], i85[11], i69[11]) → LOAD1222(i79[11] + -1, i85[11], i69[11])
(10): LOAD1232(i79[10], i85[10], i69[10]) → COND_LOAD12322(i69[10] >= 0 && i79[10] > i69[10], i79[10], i85[10], i69[10])
(13): COND_LOAD12223(TRUE, i79[13], i85[13], i69[13]) → LOAD1222(i79[13] + -1, i85[13], i69[13])
(12): LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(i69[12] >= 0 && i79[12] > i69[12], i79[12], i85[12], i69[12])
(3): COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3])
(2): LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(i85[2] <= i69[2] && i79[2] <= i69[2], i79[2], i85[2], i69[2])
(1): COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1])
(0): LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(i69[0] >= 0 && i85[0] > i69[0] && i79[0] <= i69[0], i79[0], i85[0], i69[0])

(3) -> (0), if ((i79[3] →* i79[0])∧(i69[3] →* i69[0])∧(i85[3] →* i85[0]))


(11) -> (0), if ((i79[11] + -1 →* i79[0])∧(i85[11] →* i85[0])∧(i69[11] →* i69[0]))


(13) -> (0), if ((i69[13] →* i69[0])∧(i79[13] + -1 →* i79[0])∧(i85[13] →* i85[0]))


(0) -> (1), if ((i79[0] →* i79[1])∧(i85[0] →* i85[1])∧(i69[0] →* i69[1])∧(i69[0] >= 0 && i85[0] > i69[0] && i79[0] <= i69[0] →* TRUE))


(1) -> (2), if ((i79[1] →* i79[2])∧(i69[1] →* i69[2])∧(i85[1] →* i85[2]))


(2) -> (3), if ((i85[2] →* i85[3])∧(i69[2] →* i69[3])∧(i85[2] <= i69[2] && i79[2] <= i69[2] →* TRUE)∧(i79[2] →* i79[3]))


(1) -> (10), if ((i69[1] →* i69[10])∧(i79[1] →* i79[10])∧(i85[1] →* i85[10]))


(10) -> (11), if ((i85[10] →* i85[11])∧(i69[10] >= 0 && i79[10] > i69[10] →* TRUE)∧(i69[10] →* i69[11])∧(i79[10] →* i79[11]))


(3) -> (12), if ((i85[3] →* i85[12])∧(i69[3] →* i69[12])∧(i79[3] →* i79[12]))


(11) -> (12), if ((i79[11] + -1 →* i79[12])∧(i85[11] →* i85[12])∧(i69[11] →* i69[12]))


(13) -> (12), if ((i69[13] →* i69[12])∧(i85[13] →* i85[12])∧(i79[13] + -1 →* i79[12]))


(12) -> (13), if ((i85[12] →* i85[13])∧(i69[12] →* i69[13])∧(i79[12] →* i79[13])∧(i69[12] >= 0 && i79[12] > i69[12] →* TRUE))



The set Q consists of the following terms:
Load1222(x0, x1, x2)
Cond_Load1222(TRUE, x0, x1, x2)
Load1232(x0, x1, x2)
Cond_Load1232(TRUE, x0, x1, x2)
Cond_Load12221(TRUE, x0, x1, x2)
Cond_Load12321(TRUE, x0, x1, x2)
Cond_Load12222(TRUE, x0, x1, x2)
Cond_Load12322(TRUE, x0, x1, x2)
Cond_Load12223(TRUE, x0, x1, x2)

(17) IDPNonInfProof (SOUND transformation)

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


For Pair COND_LOAD12322(TRUE, i79[11], i85[11], i69[11]) → LOAD1222(+(i79[11], -1), i85[11], i69[11]) the following chains were created:
  • We consider the chain LOAD1232(i79[10], i85[10], i69[10]) → COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10]), COND_LOAD12322(TRUE, i79[11], i85[11], i69[11]) → LOAD1222(+(i79[11], -1), i85[11], i69[11]), LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]) which results in the following constraint:

    (1)    (i85[10]=i85[11]∧&&(>=(i69[10], 0), >(i79[10], i69[10]))=TRUE∧i69[10]=i69[11]∧i79[10]=i79[11]∧+(i79[11], -1)=i79[0]∧i85[11]=i85[0]∧i69[11]=i69[0] ⇒ COND_LOAD12322(TRUE, i79[11], i85[11], i69[11])≥NonInfC∧COND_LOAD12322(TRUE, i79[11], i85[11], i69[11])≥LOAD1222(+(i79[11], -1), i85[11], i69[11])∧(UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥))



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

    (2)    (>=(i69[10], 0)=TRUE∧>(i79[10], i69[10])=TRUE ⇒ COND_LOAD12322(TRUE, i79[10], i85[10], i69[10])≥NonInfC∧COND_LOAD12322(TRUE, i79[10], i85[10], i69[10])≥LOAD1222(+(i79[10], -1), i85[10], i69[10])∧(UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥))



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

    (3)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧[(-1)bni_35 + (-1)Bound*bni_35] + [(-1)bni_35]i69[10] + [bni_35]i79[10] ≥ 0∧[1 + (-1)bso_36] ≥ 0)



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

    (4)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧[(-1)bni_35 + (-1)Bound*bni_35] + [(-1)bni_35]i69[10] + [bni_35]i79[10] ≥ 0∧[1 + (-1)bso_36] ≥ 0)



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

    (5)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧[(-1)bni_35 + (-1)Bound*bni_35] + [(-1)bni_35]i69[10] + [bni_35]i79[10] ≥ 0∧[1 + (-1)bso_36] ≥ 0)



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

    (6)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧0 = 0∧[(-1)bni_35 + (-1)Bound*bni_35] + [(-1)bni_35]i69[10] + [bni_35]i79[10] ≥ 0∧0 = 0∧[1 + (-1)bso_36] ≥ 0)



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

    (7)    (i69[10] ≥ 0∧i79[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧0 = 0∧[(-1)Bound*bni_35] + [bni_35]i79[10] ≥ 0∧0 = 0∧[1 + (-1)bso_36] ≥ 0)



  • We consider the chain LOAD1232(i79[10], i85[10], i69[10]) → COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10]), COND_LOAD12322(TRUE, i79[11], i85[11], i69[11]) → LOAD1222(+(i79[11], -1), i85[11], i69[11]), LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12]) which results in the following constraint:

    (8)    (i85[10]=i85[11]∧&&(>=(i69[10], 0), >(i79[10], i69[10]))=TRUE∧i69[10]=i69[11]∧i79[10]=i79[11]∧+(i79[11], -1)=i79[12]∧i85[11]=i85[12]∧i69[11]=i69[12] ⇒ COND_LOAD12322(TRUE, i79[11], i85[11], i69[11])≥NonInfC∧COND_LOAD12322(TRUE, i79[11], i85[11], i69[11])≥LOAD1222(+(i79[11], -1), i85[11], i69[11])∧(UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥))



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

    (9)    (>=(i69[10], 0)=TRUE∧>(i79[10], i69[10])=TRUE ⇒ COND_LOAD12322(TRUE, i79[10], i85[10], i69[10])≥NonInfC∧COND_LOAD12322(TRUE, i79[10], i85[10], i69[10])≥LOAD1222(+(i79[10], -1), i85[10], i69[10])∧(UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥))



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

    (10)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧[(-1)bni_35 + (-1)Bound*bni_35] + [(-1)bni_35]i69[10] + [bni_35]i79[10] ≥ 0∧[1 + (-1)bso_36] ≥ 0)



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

    (11)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧[(-1)bni_35 + (-1)Bound*bni_35] + [(-1)bni_35]i69[10] + [bni_35]i79[10] ≥ 0∧[1 + (-1)bso_36] ≥ 0)



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

    (12)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧[(-1)bni_35 + (-1)Bound*bni_35] + [(-1)bni_35]i69[10] + [bni_35]i79[10] ≥ 0∧[1 + (-1)bso_36] ≥ 0)



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

    (13)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧0 = 0∧[(-1)bni_35 + (-1)Bound*bni_35] + [(-1)bni_35]i69[10] + [bni_35]i79[10] ≥ 0∧0 = 0∧[1 + (-1)bso_36] ≥ 0)



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

    (14)    (i69[10] ≥ 0∧i79[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧0 = 0∧[(-1)Bound*bni_35] + [bni_35]i79[10] ≥ 0∧0 = 0∧[1 + (-1)bso_36] ≥ 0)







For Pair LOAD1232(i79[10], i85[10], i69[10]) → COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10]) the following chains were created:
  • We consider the chain LOAD1232(i79[10], i85[10], i69[10]) → COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10]), COND_LOAD12322(TRUE, i79[11], i85[11], i69[11]) → LOAD1222(+(i79[11], -1), i85[11], i69[11]) which results in the following constraint:

    (15)    (i85[10]=i85[11]∧&&(>=(i69[10], 0), >(i79[10], i69[10]))=TRUE∧i69[10]=i69[11]∧i79[10]=i79[11] ⇒ LOAD1232(i79[10], i85[10], i69[10])≥NonInfC∧LOAD1232(i79[10], i85[10], i69[10])≥COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])∧(UIncreasing(COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])), ≥))



    We simplified constraint (15) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (16)    (>=(i69[10], 0)=TRUE∧>(i79[10], i69[10])=TRUE ⇒ LOAD1232(i79[10], i85[10], i69[10])≥NonInfC∧LOAD1232(i79[10], i85[10], i69[10])≥COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])∧(UIncreasing(COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])), ≥))



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

    (17)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])), ≥)∧[(-1)bni_37 + (-1)Bound*bni_37] + [(-1)bni_37]i69[10] + [bni_37]i79[10] ≥ 0∧[(-1)bso_38] ≥ 0)



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

    (18)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])), ≥)∧[(-1)bni_37 + (-1)Bound*bni_37] + [(-1)bni_37]i69[10] + [bni_37]i79[10] ≥ 0∧[(-1)bso_38] ≥ 0)



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

    (19)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])), ≥)∧[(-1)bni_37 + (-1)Bound*bni_37] + [(-1)bni_37]i69[10] + [bni_37]i79[10] ≥ 0∧[(-1)bso_38] ≥ 0)



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

    (20)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])), ≥)∧0 = 0∧[(-1)bni_37 + (-1)Bound*bni_37] + [(-1)bni_37]i69[10] + [bni_37]i79[10] ≥ 0∧0 = 0∧[(-1)bso_38] ≥ 0)



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

    (21)    (i69[10] ≥ 0∧i79[10] ≥ 0 ⇒ (UIncreasing(COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])), ≥)∧0 = 0∧[(-1)Bound*bni_37] + [bni_37]i79[10] ≥ 0∧0 = 0∧[(-1)bso_38] ≥ 0)







For Pair COND_LOAD12223(TRUE, i79[13], i85[13], i69[13]) → LOAD1222(+(i79[13], -1), i85[13], i69[13]) the following chains were created:
  • We consider the chain LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12]), COND_LOAD12223(TRUE, i79[13], i85[13], i69[13]) → LOAD1222(+(i79[13], -1), i85[13], i69[13]), LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]) which results in the following constraint:

    (22)    (i85[12]=i85[13]∧i69[12]=i69[13]∧i79[12]=i79[13]∧&&(>=(i69[12], 0), >(i79[12], i69[12]))=TRUE∧i69[13]=i69[0]∧+(i79[13], -1)=i79[0]∧i85[13]=i85[0] ⇒ COND_LOAD12223(TRUE, i79[13], i85[13], i69[13])≥NonInfC∧COND_LOAD12223(TRUE, i79[13], i85[13], i69[13])≥LOAD1222(+(i79[13], -1), i85[13], i69[13])∧(UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥))



    We simplified constraint (22) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (23)    (>=(i69[12], 0)=TRUE∧>(i79[12], i69[12])=TRUE ⇒ COND_LOAD12223(TRUE, i79[12], i85[12], i69[12])≥NonInfC∧COND_LOAD12223(TRUE, i79[12], i85[12], i69[12])≥LOAD1222(+(i79[12], -1), i85[12], i69[12])∧(UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥))



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

    (24)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧[(-1)bni_39 + (-1)Bound*bni_39] + [(-1)bni_39]i69[12] + [bni_39]i79[12] ≥ 0∧[1 + (-1)bso_40] ≥ 0)



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

    (25)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧[(-1)bni_39 + (-1)Bound*bni_39] + [(-1)bni_39]i69[12] + [bni_39]i79[12] ≥ 0∧[1 + (-1)bso_40] ≥ 0)



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

    (26)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧[(-1)bni_39 + (-1)Bound*bni_39] + [(-1)bni_39]i69[12] + [bni_39]i79[12] ≥ 0∧[1 + (-1)bso_40] ≥ 0)



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

    (27)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧0 = 0∧[(-1)bni_39 + (-1)Bound*bni_39] + [(-1)bni_39]i69[12] + [bni_39]i79[12] ≥ 0∧0 = 0∧[1 + (-1)bso_40] ≥ 0)



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

    (28)    (i69[12] ≥ 0∧i79[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧0 = 0∧[(-1)Bound*bni_39] + [bni_39]i79[12] ≥ 0∧0 = 0∧[1 + (-1)bso_40] ≥ 0)



  • We consider the chain LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12]), COND_LOAD12223(TRUE, i79[13], i85[13], i69[13]) → LOAD1222(+(i79[13], -1), i85[13], i69[13]), LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12]) which results in the following constraint:

    (29)    (i85[12]=i85[13]∧i69[12]=i69[13]∧i79[12]=i79[13]∧&&(>=(i69[12], 0), >(i79[12], i69[12]))=TRUE∧i69[13]=i69[12]1∧i85[13]=i85[12]1∧+(i79[13], -1)=i79[12]1 ⇒ COND_LOAD12223(TRUE, i79[13], i85[13], i69[13])≥NonInfC∧COND_LOAD12223(TRUE, i79[13], i85[13], i69[13])≥LOAD1222(+(i79[13], -1), i85[13], i69[13])∧(UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥))



    We simplified constraint (29) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (30)    (>=(i69[12], 0)=TRUE∧>(i79[12], i69[12])=TRUE ⇒ COND_LOAD12223(TRUE, i79[12], i85[12], i69[12])≥NonInfC∧COND_LOAD12223(TRUE, i79[12], i85[12], i69[12])≥LOAD1222(+(i79[12], -1), i85[12], i69[12])∧(UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥))



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

    (31)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧[(-1)bni_39 + (-1)Bound*bni_39] + [(-1)bni_39]i69[12] + [bni_39]i79[12] ≥ 0∧[1 + (-1)bso_40] ≥ 0)



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

    (32)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧[(-1)bni_39 + (-1)Bound*bni_39] + [(-1)bni_39]i69[12] + [bni_39]i79[12] ≥ 0∧[1 + (-1)bso_40] ≥ 0)



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

    (33)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧[(-1)bni_39 + (-1)Bound*bni_39] + [(-1)bni_39]i69[12] + [bni_39]i79[12] ≥ 0∧[1 + (-1)bso_40] ≥ 0)



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

    (34)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧0 = 0∧[(-1)bni_39 + (-1)Bound*bni_39] + [(-1)bni_39]i69[12] + [bni_39]i79[12] ≥ 0∧0 = 0∧[1 + (-1)bso_40] ≥ 0)



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

    (35)    (i69[12] ≥ 0∧i79[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧0 = 0∧[(-1)Bound*bni_39] + [bni_39]i79[12] ≥ 0∧0 = 0∧[1 + (-1)bso_40] ≥ 0)







For Pair LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12]) the following chains were created:
  • We consider the chain LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12]), COND_LOAD12223(TRUE, i79[13], i85[13], i69[13]) → LOAD1222(+(i79[13], -1), i85[13], i69[13]) which results in the following constraint:

    (36)    (i85[12]=i85[13]∧i69[12]=i69[13]∧i79[12]=i79[13]∧&&(>=(i69[12], 0), >(i79[12], i69[12]))=TRUE ⇒ LOAD1222(i79[12], i85[12], i69[12])≥NonInfC∧LOAD1222(i79[12], i85[12], i69[12])≥COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])∧(UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥))



    We simplified constraint (36) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (37)    (>=(i69[12], 0)=TRUE∧>(i79[12], i69[12])=TRUE ⇒ LOAD1222(i79[12], i85[12], i69[12])≥NonInfC∧LOAD1222(i79[12], i85[12], i69[12])≥COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])∧(UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥))



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

    (38)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥)∧[(-1)bni_41 + (-1)Bound*bni_41] + [(-1)bni_41]i69[12] + [bni_41]i79[12] ≥ 0∧[(-1)bso_42] ≥ 0)



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

    (39)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥)∧[(-1)bni_41 + (-1)Bound*bni_41] + [(-1)bni_41]i69[12] + [bni_41]i79[12] ≥ 0∧[(-1)bso_42] ≥ 0)



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

    (40)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥)∧[(-1)bni_41 + (-1)Bound*bni_41] + [(-1)bni_41]i69[12] + [bni_41]i79[12] ≥ 0∧[(-1)bso_42] ≥ 0)



    We simplified constraint (40) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

    (41)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥)∧0 = 0∧[(-1)bni_41 + (-1)Bound*bni_41] + [(-1)bni_41]i69[12] + [bni_41]i79[12] ≥ 0∧0 = 0∧[(-1)bso_42] ≥ 0)



    We simplified constraint (41) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (42)    (i69[12] ≥ 0∧i79[12] ≥ 0 ⇒ (UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥)∧0 = 0∧[(-1)Bound*bni_41] + [bni_41]i79[12] ≥ 0∧0 = 0∧[(-1)bso_42] ≥ 0)







For Pair COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3]) the following chains were created:
  • We consider the chain COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3]), LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]) which results in the following constraint:

    (43)    (i79[3]=i79[0]∧i69[3]=i69[0]∧i85[3]=i85[0] ⇒ COND_LOAD1232(TRUE, i79[3], i85[3], i69[3])≥NonInfC∧COND_LOAD1232(TRUE, i79[3], i85[3], i69[3])≥LOAD1222(i79[3], i85[3], i69[3])∧(UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥))



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

    (44)    (COND_LOAD1232(TRUE, i79[3], i85[3], i69[3])≥NonInfC∧COND_LOAD1232(TRUE, i79[3], i85[3], i69[3])≥LOAD1222(i79[3], i85[3], i69[3])∧(UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥))



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

    (45)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bso_44] ≥ 0)



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

    (46)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bso_44] ≥ 0)



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

    (47)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bso_44] ≥ 0)



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

    (48)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_44] ≥ 0)



  • We consider the chain COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3]), LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12]) which results in the following constraint:

    (49)    (i85[3]=i85[12]∧i69[3]=i69[12]∧i79[3]=i79[12] ⇒ COND_LOAD1232(TRUE, i79[3], i85[3], i69[3])≥NonInfC∧COND_LOAD1232(TRUE, i79[3], i85[3], i69[3])≥LOAD1222(i79[3], i85[3], i69[3])∧(UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥))



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

    (50)    (COND_LOAD1232(TRUE, i79[3], i85[3], i69[3])≥NonInfC∧COND_LOAD1232(TRUE, i79[3], i85[3], i69[3])≥LOAD1222(i79[3], i85[3], i69[3])∧(UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥))



    We simplified constraint (50) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (51)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bso_44] ≥ 0)



    We simplified constraint (51) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (52)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bso_44] ≥ 0)



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

    (53)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bso_44] ≥ 0)



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

    (54)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_44] ≥ 0)







For Pair LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2]) the following chains were created:
  • We consider the chain LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2]), COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3]) which results in the following constraint:

    (55)    (i85[2]=i85[3]∧i69[2]=i69[3]∧&&(<=(i85[2], i69[2]), <=(i79[2], i69[2]))=TRUE∧i79[2]=i79[3] ⇒ LOAD1232(i79[2], i85[2], i69[2])≥NonInfC∧LOAD1232(i79[2], i85[2], i69[2])≥COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])∧(UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥))



    We simplified constraint (55) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (56)    (<=(i85[2], i69[2])=TRUE∧<=(i79[2], i69[2])=TRUE ⇒ LOAD1232(i79[2], i85[2], i69[2])≥NonInfC∧LOAD1232(i79[2], i85[2], i69[2])≥COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])∧(UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥))



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

    (57)    (i69[2] + [-1]i85[2] ≥ 0∧i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_45 + (-1)Bound*bni_45] + [(-1)bni_45]i69[2] + [bni_45]i79[2] ≥ 0∧[(-1)bso_46] ≥ 0)



    We simplified constraint (57) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (58)    (i69[2] + [-1]i85[2] ≥ 0∧i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_45 + (-1)Bound*bni_45] + [(-1)bni_45]i69[2] + [bni_45]i79[2] ≥ 0∧[(-1)bso_46] ≥ 0)



    We simplified constraint (58) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (59)    (i69[2] + [-1]i85[2] ≥ 0∧i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_45 + (-1)Bound*bni_45] + [(-1)bni_45]i69[2] + [bni_45]i79[2] ≥ 0∧[(-1)bso_46] ≥ 0)



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

    (60)    (i69[2] ≥ 0∧i85[2] + i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_45 + (-1)Bound*bni_45] + [(-1)bni_45]i85[2] + [(-1)bni_45]i69[2] + [bni_45]i79[2] ≥ 0∧[(-1)bso_46] ≥ 0)



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

    (61)    (i69[2] ≥ 0∧i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_45 + (-1)Bound*bni_45] + [(-1)bni_45]i79[2] ≥ 0∧[(-1)bso_46] ≥ 0)



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

    (62)    (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_45 + (-1)Bound*bni_45] + [(-1)bni_45]i79[2] ≥ 0∧[(-1)bso_46] ≥ 0)


    (63)    (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_45 + (-1)Bound*bni_45] + [(-1)bni_45]i79[2] ≥ 0∧[(-1)bso_46] ≥ 0)







For Pair COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1]) the following chains were created:
  • We consider the chain COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1]), LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2]) which results in the following constraint:

    (64)    (i79[1]=i79[2]∧i69[1]=i69[2]∧i85[1]=i85[2] ⇒ COND_LOAD1222(TRUE, i79[1], i85[1], i69[1])≥NonInfC∧COND_LOAD1222(TRUE, i79[1], i85[1], i69[1])≥LOAD1232(i79[1], i85[1], i69[1])∧(UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥))



    We simplified constraint (64) using rule (IV) which results in the following new constraint:

    (65)    (COND_LOAD1222(TRUE, i79[1], i85[1], i69[1])≥NonInfC∧COND_LOAD1222(TRUE, i79[1], i85[1], i69[1])≥LOAD1232(i79[1], i85[1], i69[1])∧(UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥))



    We simplified constraint (65) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (66)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_48] ≥ 0)



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

    (67)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_48] ≥ 0)



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

    (68)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_48] ≥ 0)



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

    (69)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_48] ≥ 0)



  • We consider the chain COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1]), LOAD1232(i79[10], i85[10], i69[10]) → COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10]) which results in the following constraint:

    (70)    (i69[1]=i69[10]∧i79[1]=i79[10]∧i85[1]=i85[10] ⇒ COND_LOAD1222(TRUE, i79[1], i85[1], i69[1])≥NonInfC∧COND_LOAD1222(TRUE, i79[1], i85[1], i69[1])≥LOAD1232(i79[1], i85[1], i69[1])∧(UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥))



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

    (71)    (COND_LOAD1222(TRUE, i79[1], i85[1], i69[1])≥NonInfC∧COND_LOAD1222(TRUE, i79[1], i85[1], i69[1])≥LOAD1232(i79[1], i85[1], i69[1])∧(UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥))



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

    (72)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_48] ≥ 0)



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

    (73)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_48] ≥ 0)



    We simplified constraint (73) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (74)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_48] ≥ 0)



    We simplified constraint (74) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

    (75)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_48] ≥ 0)







For Pair LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]) the following chains were created:
  • We consider the chain LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]), COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1]) which results in the following constraint:

    (76)    (i79[0]=i79[1]∧i85[0]=i85[1]∧i69[0]=i69[1]∧&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0]))=TRUE ⇒ LOAD1222(i79[0], i85[0], i69[0])≥NonInfC∧LOAD1222(i79[0], i85[0], i69[0])≥COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])∧(UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥))



    We simplified constraint (76) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (77)    (<=(i79[0], i69[0])=TRUE∧>=(i69[0], 0)=TRUE∧>(i85[0], i69[0])=TRUE ⇒ LOAD1222(i79[0], i85[0], i69[0])≥NonInfC∧LOAD1222(i79[0], i85[0], i69[0])≥COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])∧(UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥))



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

    (78)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] + [-1] + [-1]i69[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)bni_49 + (-1)Bound*bni_49] + [(-1)bni_49]i69[0] + [bni_49]i79[0] ≥ 0∧[(-1)bso_50] ≥ 0)



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

    (79)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] + [-1] + [-1]i69[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)bni_49 + (-1)Bound*bni_49] + [(-1)bni_49]i69[0] + [bni_49]i79[0] ≥ 0∧[(-1)bso_50] ≥ 0)



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

    (80)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] + [-1] + [-1]i69[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)bni_49 + (-1)Bound*bni_49] + [(-1)bni_49]i69[0] + [bni_49]i79[0] ≥ 0∧[(-1)bso_50] ≥ 0)



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

    (81)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)bni_49 + (-1)Bound*bni_49] + [(-1)bni_49]i69[0] + [bni_49]i79[0] ≥ 0∧[(-1)bso_50] ≥ 0)



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

    (82)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)bni_49 + (-1)Bound*bni_49] + [(-1)bni_49]i69[0] + [bni_49]i79[0] ≥ 0∧[(-1)bso_50] ≥ 0)


    (83)    (i69[0] + i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)bni_49 + (-1)Bound*bni_49] + [(-1)bni_49]i69[0] + [(-1)bni_49]i79[0] ≥ 0∧[(-1)bso_50] ≥ 0)



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

    (84)    (i69[0] ≥ 0∧i79[0] + i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)bni_49 + (-1)Bound*bni_49] + [(-1)bni_49]i69[0] ≥ 0∧[(-1)bso_50] ≥ 0)







To summarize, we get the following constraints P≥ for the following pairs.
  • COND_LOAD12322(TRUE, i79[11], i85[11], i69[11]) → LOAD1222(+(i79[11], -1), i85[11], i69[11])
    • (i69[10] ≥ 0∧i79[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧0 = 0∧[(-1)Bound*bni_35] + [bni_35]i79[10] ≥ 0∧0 = 0∧[1 + (-1)bso_36] ≥ 0)
    • (i69[10] ≥ 0∧i79[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧0 = 0∧[(-1)Bound*bni_35] + [bni_35]i79[10] ≥ 0∧0 = 0∧[1 + (-1)bso_36] ≥ 0)

  • LOAD1232(i79[10], i85[10], i69[10]) → COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])
    • (i69[10] ≥ 0∧i79[10] ≥ 0 ⇒ (UIncreasing(COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])), ≥)∧0 = 0∧[(-1)Bound*bni_37] + [bni_37]i79[10] ≥ 0∧0 = 0∧[(-1)bso_38] ≥ 0)

  • COND_LOAD12223(TRUE, i79[13], i85[13], i69[13]) → LOAD1222(+(i79[13], -1), i85[13], i69[13])
    • (i69[12] ≥ 0∧i79[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧0 = 0∧[(-1)Bound*bni_39] + [bni_39]i79[12] ≥ 0∧0 = 0∧[1 + (-1)bso_40] ≥ 0)
    • (i69[12] ≥ 0∧i79[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧0 = 0∧[(-1)Bound*bni_39] + [bni_39]i79[12] ≥ 0∧0 = 0∧[1 + (-1)bso_40] ≥ 0)

  • LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])
    • (i69[12] ≥ 0∧i79[12] ≥ 0 ⇒ (UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥)∧0 = 0∧[(-1)Bound*bni_41] + [bni_41]i79[12] ≥ 0∧0 = 0∧[(-1)bso_42] ≥ 0)

  • COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3])
    • ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_44] ≥ 0)
    • ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_44] ≥ 0)

  • LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])
    • (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_45 + (-1)Bound*bni_45] + [(-1)bni_45]i79[2] ≥ 0∧[(-1)bso_46] ≥ 0)
    • (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_45 + (-1)Bound*bni_45] + [(-1)bni_45]i79[2] ≥ 0∧[(-1)bso_46] ≥ 0)

  • COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1])
    • ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_48] ≥ 0)
    • ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_48] ≥ 0)

  • LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])
    • (i69[0] + i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)bni_49 + (-1)Bound*bni_49] + [(-1)bni_49]i69[0] + [(-1)bni_49]i79[0] ≥ 0∧[(-1)bso_50] ≥ 0)
    • (i69[0] ≥ 0∧i79[0] + i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)bni_49 + (-1)Bound*bni_49] + [(-1)bni_49]i69[0] ≥ 0∧[(-1)bso_50] ≥ 0)




The constraints for P> respective Pbound are constructed from P≥ where we just replace every occurence of "t ≥ s" in P≥ by "t > s" respective "t ≥ c". Here c stands for the fresh constant used for Pbound.
Using the following integer polynomial ordering the resulting constraints can be solved
Polynomial interpretation over integers[POLO]:

POL(TRUE) = 0   
POL(FALSE) = 0   
POL(COND_LOAD12322(x1, x2, x3, x4)) = [-1] + [-1]x4 + x2   
POL(LOAD1222(x1, x2, x3)) = [-1] + [-1]x3 + x1   
POL(+(x1, x2)) = x1 + x2   
POL(-1) = [-1]   
POL(LOAD1232(x1, x2, x3)) = [-1] + [-1]x3 + x1   
POL(&&(x1, x2)) = [-1]   
POL(>=(x1, x2)) = [-1]   
POL(0) = 0   
POL(>(x1, x2)) = [-1]   
POL(COND_LOAD12223(x1, x2, x3, x4)) = [-1] + [-1]x4 + x2   
POL(COND_LOAD1232(x1, x2, x3, x4)) = [-1] + [-1]x4 + x2   
POL(<=(x1, x2)) = [-1]   
POL(COND_LOAD1222(x1, x2, x3, x4)) = [-1] + [-1]x4 + x2   

The following pairs are in P>:

COND_LOAD12322(TRUE, i79[11], i85[11], i69[11]) → LOAD1222(+(i79[11], -1), i85[11], i69[11])
COND_LOAD12223(TRUE, i79[13], i85[13], i69[13]) → LOAD1222(+(i79[13], -1), i85[13], i69[13])

The following pairs are in Pbound:

COND_LOAD12322(TRUE, i79[11], i85[11], i69[11]) → LOAD1222(+(i79[11], -1), i85[11], i69[11])
LOAD1232(i79[10], i85[10], i69[10]) → COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])
COND_LOAD12223(TRUE, i79[13], i85[13], i69[13]) → LOAD1222(+(i79[13], -1), i85[13], i69[13])
LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])

The following pairs are in P≥:

LOAD1232(i79[10], i85[10], i69[10]) → COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])
LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])
COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3])
LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])
COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1])
LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])

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

(18) Complex Obligation (AND)

(19) Obligation:

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


The following domains are used:

Boolean, Integer


R is empty.

The integer pair graph contains the following rules and edges:
(10): LOAD1232(i79[10], i85[10], i69[10]) → COND_LOAD12322(i69[10] >= 0 && i79[10] > i69[10], i79[10], i85[10], i69[10])
(12): LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(i69[12] >= 0 && i79[12] > i69[12], i79[12], i85[12], i69[12])
(3): COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3])
(2): LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(i85[2] <= i69[2] && i79[2] <= i69[2], i79[2], i85[2], i69[2])
(1): COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1])
(0): LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(i69[0] >= 0 && i85[0] > i69[0] && i79[0] <= i69[0], i79[0], i85[0], i69[0])

(3) -> (0), if ((i79[3] →* i79[0])∧(i69[3] →* i69[0])∧(i85[3] →* i85[0]))


(0) -> (1), if ((i79[0] →* i79[1])∧(i85[0] →* i85[1])∧(i69[0] →* i69[1])∧(i69[0] >= 0 && i85[0] > i69[0] && i79[0] <= i69[0] →* TRUE))


(1) -> (2), if ((i79[1] →* i79[2])∧(i69[1] →* i69[2])∧(i85[1] →* i85[2]))


(2) -> (3), if ((i85[2] →* i85[3])∧(i69[2] →* i69[3])∧(i85[2] <= i69[2] && i79[2] <= i69[2] →* TRUE)∧(i79[2] →* i79[3]))


(1) -> (10), if ((i69[1] →* i69[10])∧(i79[1] →* i79[10])∧(i85[1] →* i85[10]))


(3) -> (12), if ((i85[3] →* i85[12])∧(i69[3] →* i69[12])∧(i79[3] →* i79[12]))



The set Q consists of the following terms:
Load1222(x0, x1, x2)
Cond_Load1222(TRUE, x0, x1, x2)
Load1232(x0, x1, x2)
Cond_Load1232(TRUE, x0, x1, x2)
Cond_Load12221(TRUE, x0, x1, x2)
Cond_Load12321(TRUE, x0, x1, x2)
Cond_Load12222(TRUE, x0, x1, x2)
Cond_Load12322(TRUE, x0, x1, x2)
Cond_Load12223(TRUE, x0, x1, x2)

(20) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes.

(21) Obligation:

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


The following domains are used:

Boolean, Integer


R is empty.

The integer pair graph contains the following rules and edges:
(2): LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(i85[2] <= i69[2] && i79[2] <= i69[2], i79[2], i85[2], i69[2])
(1): COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1])
(0): LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(i69[0] >= 0 && i85[0] > i69[0] && i79[0] <= i69[0], i79[0], i85[0], i69[0])
(3): COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3])

(3) -> (0), if ((i79[3] →* i79[0])∧(i69[3] →* i69[0])∧(i85[3] →* i85[0]))


(0) -> (1), if ((i79[0] →* i79[1])∧(i85[0] →* i85[1])∧(i69[0] →* i69[1])∧(i69[0] >= 0 && i85[0] > i69[0] && i79[0] <= i69[0] →* TRUE))


(1) -> (2), if ((i79[1] →* i79[2])∧(i69[1] →* i69[2])∧(i85[1] →* i85[2]))


(2) -> (3), if ((i85[2] →* i85[3])∧(i69[2] →* i69[3])∧(i85[2] <= i69[2] && i79[2] <= i69[2] →* TRUE)∧(i79[2] →* i79[3]))



The set Q consists of the following terms:
Load1222(x0, x1, x2)
Cond_Load1222(TRUE, x0, x1, x2)
Load1232(x0, x1, x2)
Cond_Load1232(TRUE, x0, x1, x2)
Cond_Load12221(TRUE, x0, x1, x2)
Cond_Load12321(TRUE, x0, x1, x2)
Cond_Load12222(TRUE, x0, x1, x2)
Cond_Load12322(TRUE, x0, x1, x2)
Cond_Load12223(TRUE, x0, x1, x2)

(22) 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 LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2]) the following chains were created:
  • We consider the chain COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1]), LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2]), COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3]) which results in the following constraint:

    (1)    (i79[1]=i79[2]∧i69[1]=i69[2]∧i85[1]=i85[2]∧i85[2]=i85[3]∧i69[2]=i69[3]∧&&(<=(i85[2], i69[2]), <=(i79[2], i69[2]))=TRUE∧i79[2]=i79[3] ⇒ LOAD1232(i79[2], i85[2], i69[2])≥NonInfC∧LOAD1232(i79[2], i85[2], i69[2])≥COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])∧(UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥))



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

    (2)    (<=(i85[2], i69[2])=TRUE∧<=(i79[2], i69[2])=TRUE ⇒ LOAD1232(i79[2], i85[2], i69[2])≥NonInfC∧LOAD1232(i79[2], i85[2], i69[2])≥COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])∧(UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥))



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

    (3)    (i69[2] + [-1]i85[2] ≥ 0∧i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_25 + (-1)Bound*bni_25] + [(2)bni_25]i69[2] + [(-1)bni_25]i85[2] + [(-1)bni_25]i79[2] ≥ 0∧[(-1)bso_26] ≥ 0)



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

    (4)    (i69[2] + [-1]i85[2] ≥ 0∧i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_25 + (-1)Bound*bni_25] + [(2)bni_25]i69[2] + [(-1)bni_25]i85[2] + [(-1)bni_25]i79[2] ≥ 0∧[(-1)bso_26] ≥ 0)



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

    (5)    (i69[2] + [-1]i85[2] ≥ 0∧i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_25 + (-1)Bound*bni_25] + [(2)bni_25]i69[2] + [(-1)bni_25]i85[2] + [(-1)bni_25]i79[2] ≥ 0∧[(-1)bso_26] ≥ 0)



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

    (6)    (i69[2] ≥ 0∧i85[2] + i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_25 + (-1)Bound*bni_25] + [bni_25]i85[2] + [(2)bni_25]i69[2] + [(-1)bni_25]i79[2] ≥ 0∧[(-1)bso_26] ≥ 0)



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

    (7)    (i69[2] ≥ 0∧i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_25 + (-1)Bound*bni_25] + [bni_25]i69[2] + [bni_25]i79[2] ≥ 0∧[(-1)bso_26] ≥ 0)



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

    (8)    (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_25 + (-1)Bound*bni_25] + [bni_25]i69[2] + [bni_25]i79[2] ≥ 0∧[(-1)bso_26] ≥ 0)


    (9)    (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_25 + (-1)Bound*bni_25] + [bni_25]i69[2] + [bni_25]i79[2] ≥ 0∧[(-1)bso_26] ≥ 0)







For Pair COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1]) the following chains were created:
  • We consider the chain LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]), COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1]), LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2]) which results in the following constraint:

    (10)    (i79[0]=i79[1]∧i85[0]=i85[1]∧i69[0]=i69[1]∧&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0]))=TRUE∧i79[1]=i79[2]∧i69[1]=i69[2]∧i85[1]=i85[2] ⇒ COND_LOAD1222(TRUE, i79[1], i85[1], i69[1])≥NonInfC∧COND_LOAD1222(TRUE, i79[1], i85[1], i69[1])≥LOAD1232(i79[1], i85[1], i69[1])∧(UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥))



    We simplified constraint (10) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (11)    (<=(i79[0], i69[0])=TRUE∧>=(i69[0], 0)=TRUE∧>(i85[0], i69[0])=TRUE ⇒ COND_LOAD1222(TRUE, i79[0], i85[0], i69[0])≥NonInfC∧COND_LOAD1222(TRUE, i79[0], i85[0], i69[0])≥LOAD1232(i79[0], i85[0], i69[0])∧(UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥))



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

    (12)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] + [-1] + [-1]i69[0] ≥ 0 ⇒ (UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bni_27 + (-1)Bound*bni_27] + [bni_27]i69[0] + [(-1)bni_27]i79[0] ≥ 0∧[(-1)bso_28] + [-1]i69[0] + i85[0] ≥ 0)



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

    (13)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] + [-1] + [-1]i69[0] ≥ 0 ⇒ (UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bni_27 + (-1)Bound*bni_27] + [bni_27]i69[0] + [(-1)bni_27]i79[0] ≥ 0∧[(-1)bso_28] + [-1]i69[0] + i85[0] ≥ 0)



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

    (14)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] + [-1] + [-1]i69[0] ≥ 0 ⇒ (UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bni_27 + (-1)Bound*bni_27] + [bni_27]i69[0] + [(-1)bni_27]i79[0] ≥ 0∧[(-1)bso_28] + [-1]i69[0] + i85[0] ≥ 0)



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

    (15)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0 ⇒ (UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bni_27 + (-1)Bound*bni_27] + [bni_27]i69[0] + [(-1)bni_27]i79[0] ≥ 0∧[1 + (-1)bso_28] + i85[0] ≥ 0)



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

    (16)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bni_27 + (-1)Bound*bni_27] + [bni_27]i69[0] + [(-1)bni_27]i79[0] ≥ 0∧[1 + (-1)bso_28] + i85[0] ≥ 0)


    (17)    (i69[0] + i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bni_27 + (-1)Bound*bni_27] + [bni_27]i69[0] + [bni_27]i79[0] ≥ 0∧[1 + (-1)bso_28] + i85[0] ≥ 0)



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

    (18)    (i69[0] ≥ 0∧i79[0] + i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bni_27 + (-1)Bound*bni_27] + [bni_27]i69[0] ≥ 0∧[1 + (-1)bso_28] + i85[0] ≥ 0)







For Pair LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]) the following chains were created:
  • We consider the chain COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3]), LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]), COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1]) which results in the following constraint:

    (19)    (i79[3]=i79[0]∧i69[3]=i69[0]∧i85[3]=i85[0]∧i79[0]=i79[1]∧i85[0]=i85[1]∧i69[0]=i69[1]∧&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0]))=TRUE ⇒ LOAD1222(i79[0], i85[0], i69[0])≥NonInfC∧LOAD1222(i79[0], i85[0], i69[0])≥COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])∧(UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥))



    We simplified constraint (19) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (20)    (<=(i79[0], i69[0])=TRUE∧>=(i69[0], 0)=TRUE∧>(i85[0], i69[0])=TRUE ⇒ LOAD1222(i79[0], i85[0], i69[0])≥NonInfC∧LOAD1222(i79[0], i85[0], i69[0])≥COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])∧(UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥))



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

    (21)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] + [-1] + [-1]i69[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)bni_29 + (-1)Bound*bni_29] + [bni_29]i85[0] + [(-1)bni_29]i79[0] ≥ 0∧[-1 + (-1)bso_30] + [-1]i69[0] + i85[0] ≥ 0)



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

    (22)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] + [-1] + [-1]i69[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)bni_29 + (-1)Bound*bni_29] + [bni_29]i85[0] + [(-1)bni_29]i79[0] ≥ 0∧[-1 + (-1)bso_30] + [-1]i69[0] + i85[0] ≥ 0)



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

    (23)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] + [-1] + [-1]i69[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)bni_29 + (-1)Bound*bni_29] + [bni_29]i85[0] + [(-1)bni_29]i79[0] ≥ 0∧[-1 + (-1)bso_30] + [-1]i69[0] + i85[0] ≥ 0)



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

    (24)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_29] + [bni_29]i69[0] + [bni_29]i85[0] + [(-1)bni_29]i79[0] ≥ 0∧[(-1)bso_30] + i85[0] ≥ 0)



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

    (25)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_29] + [bni_29]i69[0] + [bni_29]i85[0] + [(-1)bni_29]i79[0] ≥ 0∧[(-1)bso_30] + i85[0] ≥ 0)


    (26)    (i69[0] + i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_29] + [bni_29]i69[0] + [bni_29]i85[0] + [bni_29]i79[0] ≥ 0∧[(-1)bso_30] + i85[0] ≥ 0)



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

    (27)    (i69[0] ≥ 0∧i79[0] + i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_29] + [bni_29]i69[0] + [bni_29]i85[0] ≥ 0∧[(-1)bso_30] + i85[0] ≥ 0)







For Pair COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3]) the following chains were created:
  • We consider the chain LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2]), COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3]), LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]) which results in the following constraint:

    (28)    (i85[2]=i85[3]∧i69[2]=i69[3]∧&&(<=(i85[2], i69[2]), <=(i79[2], i69[2]))=TRUE∧i79[2]=i79[3]∧i79[3]=i79[0]∧i69[3]=i69[0]∧i85[3]=i85[0] ⇒ COND_LOAD1232(TRUE, i79[3], i85[3], i69[3])≥NonInfC∧COND_LOAD1232(TRUE, i79[3], i85[3], i69[3])≥LOAD1222(i79[3], i85[3], i69[3])∧(UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥))



    We simplified constraint (28) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (29)    (<=(i85[2], i69[2])=TRUE∧<=(i79[2], i69[2])=TRUE ⇒ COND_LOAD1232(TRUE, i79[2], i85[2], i69[2])≥NonInfC∧COND_LOAD1232(TRUE, i79[2], i85[2], i69[2])≥LOAD1222(i79[2], i85[2], i69[2])∧(UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥))



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

    (30)    (i69[2] + [-1]i85[2] ≥ 0∧i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bni_31 + (-1)Bound*bni_31] + [(2)bni_31]i69[2] + [(-1)bni_31]i85[2] + [(-1)bni_31]i79[2] ≥ 0∧[(-1)bso_32] + [2]i69[2] + [-2]i85[2] ≥ 0)



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

    (31)    (i69[2] + [-1]i85[2] ≥ 0∧i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bni_31 + (-1)Bound*bni_31] + [(2)bni_31]i69[2] + [(-1)bni_31]i85[2] + [(-1)bni_31]i79[2] ≥ 0∧[(-1)bso_32] + [2]i69[2] + [-2]i85[2] ≥ 0)



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

    (32)    (i69[2] + [-1]i85[2] ≥ 0∧i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bni_31 + (-1)Bound*bni_31] + [(2)bni_31]i69[2] + [(-1)bni_31]i85[2] + [(-1)bni_31]i79[2] ≥ 0∧[(-1)bso_32] + [2]i69[2] + [-2]i85[2] ≥ 0)



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

    (33)    (i69[2] ≥ 0∧i85[2] + i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bni_31 + (-1)Bound*bni_31] + [bni_31]i85[2] + [(2)bni_31]i69[2] + [(-1)bni_31]i79[2] ≥ 0∧[(-1)bso_32] + [2]i69[2] ≥ 0)



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

    (34)    (i69[2] ≥ 0∧i79[2] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bni_31 + (-1)Bound*bni_31] + [bni_31]i69[2] + [bni_31]i79[2] ≥ 0∧[(-1)bso_32] + [2]i69[2] ≥ 0)



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

    (35)    (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bni_31 + (-1)Bound*bni_31] + [bni_31]i69[2] + [bni_31]i79[2] ≥ 0∧[(-1)bso_32] + [2]i69[2] ≥ 0)


    (36)    (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bni_31 + (-1)Bound*bni_31] + [bni_31]i69[2] + [bni_31]i79[2] ≥ 0∧[(-1)bso_32] + [2]i69[2] ≥ 0)







To summarize, we get the following constraints P≥ for the following pairs.
  • LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])
    • (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_25 + (-1)Bound*bni_25] + [bni_25]i69[2] + [bni_25]i79[2] ≥ 0∧[(-1)bso_26] ≥ 0)
    • (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_25 + (-1)Bound*bni_25] + [bni_25]i69[2] + [bni_25]i79[2] ≥ 0∧[(-1)bso_26] ≥ 0)

  • COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1])
    • (i69[0] + i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bni_27 + (-1)Bound*bni_27] + [bni_27]i69[0] + [bni_27]i79[0] ≥ 0∧[1 + (-1)bso_28] + i85[0] ≥ 0)
    • (i69[0] ≥ 0∧i79[0] + i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bni_27 + (-1)Bound*bni_27] + [bni_27]i69[0] ≥ 0∧[1 + (-1)bso_28] + i85[0] ≥ 0)

  • LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])
    • (i69[0] + i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_29] + [bni_29]i69[0] + [bni_29]i85[0] + [bni_29]i79[0] ≥ 0∧[(-1)bso_30] + i85[0] ≥ 0)
    • (i69[0] ≥ 0∧i79[0] + i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_29] + [bni_29]i69[0] + [bni_29]i85[0] ≥ 0∧[(-1)bso_30] + i85[0] ≥ 0)

  • COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3])
    • (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bni_31 + (-1)Bound*bni_31] + [bni_31]i69[2] + [bni_31]i79[2] ≥ 0∧[(-1)bso_32] + [2]i69[2] ≥ 0)
    • (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bni_31 + (-1)Bound*bni_31] + [bni_31]i69[2] + [bni_31]i79[2] ≥ 0∧[(-1)bso_32] + [2]i69[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(LOAD1232(x1, x2, x3)) = [-1] + [2]x3 + [-1]x2 + [-1]x1   
POL(COND_LOAD1232(x1, x2, x3, x4)) = [-1] + [2]x4 + [-1]x3 + [-1]x2   
POL(&&(x1, x2)) = [-1]   
POL(<=(x1, x2)) = [-1]   
POL(COND_LOAD1222(x1, x2, x3, x4)) = [-1] + x4 + [-1]x2 + [-1]x1   
POL(LOAD1222(x1, x2, x3)) = [-1] + x2 + [-1]x1   
POL(>=(x1, x2)) = [-1]   
POL(0) = 0   
POL(>(x1, x2)) = [-1]   

The following pairs are in P>:

COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1])

The following pairs are in Pbound:

LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])
COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1])
LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])
COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3])

The following pairs are in P≥:

LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])
LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])
COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3])

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

(23) Complex Obligation (AND)

(24) Obligation:

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


The following domains are used:

Boolean, Integer


R is empty.

The integer pair graph contains the following rules and edges:
(2): LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(i85[2] <= i69[2] && i79[2] <= i69[2], i79[2], i85[2], i69[2])
(0): LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(i69[0] >= 0 && i85[0] > i69[0] && i79[0] <= i69[0], i79[0], i85[0], i69[0])
(3): COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3])

(3) -> (0), if ((i79[3] →* i79[0])∧(i69[3] →* i69[0])∧(i85[3] →* i85[0]))


(2) -> (3), if ((i85[2] →* i85[3])∧(i69[2] →* i69[3])∧(i85[2] <= i69[2] && i79[2] <= i69[2] →* TRUE)∧(i79[2] →* i79[3]))



The set Q consists of the following terms:
Load1222(x0, x1, x2)
Cond_Load1222(TRUE, x0, x1, x2)
Load1232(x0, x1, x2)
Cond_Load1232(TRUE, x0, x1, x2)
Cond_Load12221(TRUE, x0, x1, x2)
Cond_Load12321(TRUE, x0, x1, x2)
Cond_Load12222(TRUE, x0, x1, x2)
Cond_Load12322(TRUE, x0, x1, x2)
Cond_Load12223(TRUE, x0, x1, x2)

(25) IDependencyGraphProof (EQUIVALENT transformation)

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

(26) TRUE

(27) Obligation:

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


The following domains are used:
none


R is empty.

The integer pair graph is empty.

The set Q consists of the following terms:
Load1222(x0, x1, x2)
Cond_Load1222(TRUE, x0, x1, x2)
Load1232(x0, x1, x2)
Cond_Load1232(TRUE, x0, x1, x2)
Cond_Load12221(TRUE, x0, x1, x2)
Cond_Load12321(TRUE, x0, x1, x2)
Cond_Load12222(TRUE, x0, x1, x2)
Cond_Load12322(TRUE, x0, x1, x2)
Cond_Load12223(TRUE, x0, x1, x2)

(28) IDependencyGraphProof (EQUIVALENT transformation)

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

(29) TRUE

(30) Obligation:

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


The following domains are used:

Boolean, Integer


R is empty.

The integer pair graph contains the following rules and edges:
(3): COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3])
(2): LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(i85[2] <= i69[2] && i79[2] <= i69[2], i79[2], i85[2], i69[2])
(1): COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1])
(0): LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(i69[0] >= 0 && i85[0] > i69[0] && i79[0] <= i69[0], i79[0], i85[0], i69[0])

(3) -> (0), if ((i79[3] →* i79[0])∧(i69[3] →* i69[0])∧(i85[3] →* i85[0]))


(0) -> (1), if ((i79[0] →* i79[1])∧(i85[0] →* i85[1])∧(i69[0] →* i69[1])∧(i69[0] >= 0 && i85[0] > i69[0] && i79[0] <= i69[0] →* TRUE))


(1) -> (2), if ((i79[1] →* i79[2])∧(i69[1] →* i69[2])∧(i85[1] →* i85[2]))


(2) -> (3), if ((i85[2] →* i85[3])∧(i69[2] →* i69[3])∧(i85[2] <= i69[2] && i79[2] <= i69[2] →* TRUE)∧(i79[2] →* i79[3]))



The set Q consists of the following terms:
Load1222(x0, x1, x2)
Cond_Load1222(TRUE, x0, x1, x2)
Load1232(x0, x1, x2)
Cond_Load1232(TRUE, x0, x1, x2)
Cond_Load12221(TRUE, x0, x1, x2)
Cond_Load12321(TRUE, x0, x1, x2)
Cond_Load12222(TRUE, x0, x1, x2)
Cond_Load12322(TRUE, x0, x1, x2)
Cond_Load12223(TRUE, x0, x1, x2)

(31) IDPNonInfProof (SOUND transformation)

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


For Pair COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3]) the following chains were created:
  • We consider the chain LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2]), COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3]), LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]) which results in the following constraint:

    (1)    (i85[2]=i85[3]∧i69[2]=i69[3]∧&&(<=(i85[2], i69[2]), <=(i79[2], i69[2]))=TRUE∧i79[2]=i79[3]∧i79[3]=i79[0]∧i69[3]=i69[0]∧i85[3]=i85[0] ⇒ COND_LOAD1232(TRUE, i79[3], i85[3], i69[3])≥NonInfC∧COND_LOAD1232(TRUE, i79[3], i85[3], i69[3])≥LOAD1222(i79[3], i85[3], i69[3])∧(UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥))



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

    (2)    (<=(i85[2], i69[2])=TRUE∧<=(i79[2], i69[2])=TRUE ⇒ COND_LOAD1232(TRUE, i79[2], i85[2], i69[2])≥NonInfC∧COND_LOAD1232(TRUE, i79[2], i85[2], i69[2])≥LOAD1222(i79[2], i85[2], i69[2])∧(UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥))



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

    (3)    (i69[2] + [-1]i85[2] ≥ 0∧i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bni_25 + (-1)Bound*bni_25] + [bni_25]i69[2] + [(-1)bni_25]i85[2] ≥ 0∧[(-1)bso_26] + [2]i69[2] + [-2]i85[2] ≥ 0)



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

    (4)    (i69[2] + [-1]i85[2] ≥ 0∧i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bni_25 + (-1)Bound*bni_25] + [bni_25]i69[2] + [(-1)bni_25]i85[2] ≥ 0∧[(-1)bso_26] + [2]i69[2] + [-2]i85[2] ≥ 0)



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

    (5)    (i69[2] + [-1]i85[2] ≥ 0∧i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bni_25 + (-1)Bound*bni_25] + [bni_25]i69[2] + [(-1)bni_25]i85[2] ≥ 0∧[(-1)bso_26] + [2]i69[2] + [-2]i85[2] ≥ 0)



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

    (6)    (i69[2] ≥ 0∧i85[2] + i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bni_25 + (-1)Bound*bni_25] + [bni_25]i69[2] ≥ 0∧[(-1)bso_26] + [2]i69[2] ≥ 0)



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

    (7)    (i69[2] ≥ 0∧i79[2] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bni_25 + (-1)Bound*bni_25] + [bni_25]i69[2] ≥ 0∧[(-1)bso_26] + [2]i69[2] ≥ 0)



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

    (8)    (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bni_25 + (-1)Bound*bni_25] + [bni_25]i69[2] ≥ 0∧[(-1)bso_26] + [2]i69[2] ≥ 0)


    (9)    (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bni_25 + (-1)Bound*bni_25] + [bni_25]i69[2] ≥ 0∧[(-1)bso_26] + [2]i69[2] ≥ 0)







For Pair LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2]) the following chains were created:
  • We consider the chain COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1]), LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2]), COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3]) which results in the following constraint:

    (10)    (i79[1]=i79[2]∧i69[1]=i69[2]∧i85[1]=i85[2]∧i85[2]=i85[3]∧i69[2]=i69[3]∧&&(<=(i85[2], i69[2]), <=(i79[2], i69[2]))=TRUE∧i79[2]=i79[3] ⇒ LOAD1232(i79[2], i85[2], i69[2])≥NonInfC∧LOAD1232(i79[2], i85[2], i69[2])≥COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])∧(UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥))



    We simplified constraint (10) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (11)    (<=(i85[2], i69[2])=TRUE∧<=(i79[2], i69[2])=TRUE ⇒ LOAD1232(i79[2], i85[2], i69[2])≥NonInfC∧LOAD1232(i79[2], i85[2], i69[2])≥COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])∧(UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥))



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

    (12)    (i69[2] + [-1]i85[2] ≥ 0∧i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_27 + (-1)Bound*bni_27] + [bni_27]i69[2] + [(-1)bni_27]i85[2] ≥ 0∧[(-1)bso_28] ≥ 0)



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

    (13)    (i69[2] + [-1]i85[2] ≥ 0∧i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_27 + (-1)Bound*bni_27] + [bni_27]i69[2] + [(-1)bni_27]i85[2] ≥ 0∧[(-1)bso_28] ≥ 0)



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

    (14)    (i69[2] + [-1]i85[2] ≥ 0∧i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_27 + (-1)Bound*bni_27] + [bni_27]i69[2] + [(-1)bni_27]i85[2] ≥ 0∧[(-1)bso_28] ≥ 0)



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

    (15)    (i69[2] ≥ 0∧i85[2] + i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_27 + (-1)Bound*bni_27] + [bni_27]i69[2] ≥ 0∧[(-1)bso_28] ≥ 0)



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

    (16)    (i69[2] ≥ 0∧i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_27 + (-1)Bound*bni_27] + [bni_27]i69[2] ≥ 0∧[(-1)bso_28] ≥ 0)



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

    (17)    (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_27 + (-1)Bound*bni_27] + [bni_27]i69[2] ≥ 0∧[(-1)bso_28] ≥ 0)


    (18)    (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_27 + (-1)Bound*bni_27] + [bni_27]i69[2] ≥ 0∧[(-1)bso_28] ≥ 0)







For Pair COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1]) the following chains were created:
  • We consider the chain LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]), COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1]), LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2]) which results in the following constraint:

    (19)    (i79[0]=i79[1]∧i85[0]=i85[1]∧i69[0]=i69[1]∧&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0]))=TRUE∧i79[1]=i79[2]∧i69[1]=i69[2]∧i85[1]=i85[2] ⇒ COND_LOAD1222(TRUE, i79[1], i85[1], i69[1])≥NonInfC∧COND_LOAD1222(TRUE, i79[1], i85[1], i69[1])≥LOAD1232(i79[1], i85[1], i69[1])∧(UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥))



    We simplified constraint (19) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (20)    (<=(i79[0], i69[0])=TRUE∧>=(i69[0], 0)=TRUE∧>(i85[0], i69[0])=TRUE ⇒ COND_LOAD1222(TRUE, i79[0], i85[0], i69[0])≥NonInfC∧COND_LOAD1222(TRUE, i79[0], i85[0], i69[0])≥LOAD1232(i79[0], i85[0], i69[0])∧(UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥))



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

    (21)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] + [-1] + [-1]i69[0] ≥ 0 ⇒ (UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bni_29 + (-1)Bound*bni_29] + [bni_29]i69[0] + [(-1)bni_29]i85[0] ≥ 0∧[(-1)bso_30] ≥ 0)



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

    (22)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] + [-1] + [-1]i69[0] ≥ 0 ⇒ (UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bni_29 + (-1)Bound*bni_29] + [bni_29]i69[0] + [(-1)bni_29]i85[0] ≥ 0∧[(-1)bso_30] ≥ 0)



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

    (23)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] + [-1] + [-1]i69[0] ≥ 0 ⇒ (UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bni_29 + (-1)Bound*bni_29] + [bni_29]i69[0] + [(-1)bni_29]i85[0] ≥ 0∧[(-1)bso_30] ≥ 0)



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

    (24)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0 ⇒ (UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-2)bni_29 + (-1)Bound*bni_29] + [(-1)bni_29]i85[0] ≥ 0∧[(-1)bso_30] ≥ 0)



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

    (25)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-2)bni_29 + (-1)Bound*bni_29] + [(-1)bni_29]i85[0] ≥ 0∧[(-1)bso_30] ≥ 0)


    (26)    (i69[0] + i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-2)bni_29 + (-1)Bound*bni_29] + [(-1)bni_29]i85[0] ≥ 0∧[(-1)bso_30] ≥ 0)



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

    (27)    (i69[0] ≥ 0∧i79[0] + i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-2)bni_29 + (-1)Bound*bni_29] + [(-1)bni_29]i85[0] ≥ 0∧[(-1)bso_30] ≥ 0)







For Pair LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]) the following chains were created:
  • We consider the chain COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3]), LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]), COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1]) which results in the following constraint:

    (28)    (i79[3]=i79[0]∧i69[3]=i69[0]∧i85[3]=i85[0]∧i79[0]=i79[1]∧i85[0]=i85[1]∧i69[0]=i69[1]∧&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0]))=TRUE ⇒ LOAD1222(i79[0], i85[0], i69[0])≥NonInfC∧LOAD1222(i79[0], i85[0], i69[0])≥COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])∧(UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥))



    We simplified constraint (28) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (29)    (<=(i79[0], i69[0])=TRUE∧>=(i69[0], 0)=TRUE∧>(i85[0], i69[0])=TRUE ⇒ LOAD1222(i79[0], i85[0], i69[0])≥NonInfC∧LOAD1222(i79[0], i85[0], i69[0])≥COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])∧(UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥))



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

    (30)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] + [-1] + [-1]i69[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)bni_31 + (-1)Bound*bni_31] + [(-1)bni_31]i69[0] + [bni_31]i85[0] ≥ 0∧[-1 + (-1)bso_32] + [-2]i69[0] + [2]i85[0] ≥ 0)



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

    (31)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] + [-1] + [-1]i69[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)bni_31 + (-1)Bound*bni_31] + [(-1)bni_31]i69[0] + [bni_31]i85[0] ≥ 0∧[-1 + (-1)bso_32] + [-2]i69[0] + [2]i85[0] ≥ 0)



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

    (32)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] + [-1] + [-1]i69[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)bni_31 + (-1)Bound*bni_31] + [(-1)bni_31]i69[0] + [bni_31]i85[0] ≥ 0∧[-1 + (-1)bso_32] + [-2]i69[0] + [2]i85[0] ≥ 0)



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

    (33)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_31] + [bni_31]i85[0] ≥ 0∧[1 + (-1)bso_32] + [2]i85[0] ≥ 0)



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

    (34)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_31] + [bni_31]i85[0] ≥ 0∧[1 + (-1)bso_32] + [2]i85[0] ≥ 0)


    (35)    (i69[0] + i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_31] + [bni_31]i85[0] ≥ 0∧[1 + (-1)bso_32] + [2]i85[0] ≥ 0)



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

    (36)    (i69[0] ≥ 0∧i79[0] + i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_31] + [bni_31]i85[0] ≥ 0∧[1 + (-1)bso_32] + [2]i85[0] ≥ 0)







To summarize, we get the following constraints P≥ for the following pairs.
  • COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3])
    • (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bni_25 + (-1)Bound*bni_25] + [bni_25]i69[2] ≥ 0∧[(-1)bso_26] + [2]i69[2] ≥ 0)
    • (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bni_25 + (-1)Bound*bni_25] + [bni_25]i69[2] ≥ 0∧[(-1)bso_26] + [2]i69[2] ≥ 0)

  • LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])
    • (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_27 + (-1)Bound*bni_27] + [bni_27]i69[2] ≥ 0∧[(-1)bso_28] ≥ 0)
    • (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_27 + (-1)Bound*bni_27] + [bni_27]i69[2] ≥ 0∧[(-1)bso_28] ≥ 0)

  • COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1])
    • (i69[0] + i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-2)bni_29 + (-1)Bound*bni_29] + [(-1)bni_29]i85[0] ≥ 0∧[(-1)bso_30] ≥ 0)
    • (i69[0] ≥ 0∧i79[0] + i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-2)bni_29 + (-1)Bound*bni_29] + [(-1)bni_29]i85[0] ≥ 0∧[(-1)bso_30] ≥ 0)

  • LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])
    • (i69[0] + i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_31] + [bni_31]i85[0] ≥ 0∧[1 + (-1)bso_32] + [2]i85[0] ≥ 0)
    • (i69[0] ≥ 0∧i79[0] + i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_31] + [bni_31]i85[0] ≥ 0∧[1 + (-1)bso_32] + [2]i85[0] ≥ 0)




The constraints for P> respective Pbound are constructed from P≥ where we just replace every occurence of "t ≥ s" in P≥ by "t > s" respective "t ≥ c". Here c stands for the fresh constant used for Pbound.
Using the following integer polynomial ordering the resulting constraints can be solved
Polynomial interpretation over integers[POLO]:

POL(TRUE) = 0   
POL(FALSE) = 0   
POL(COND_LOAD1232(x1, x2, x3, x4)) = [-1] + x4 + [-1]x3   
POL(LOAD1222(x1, x2, x3)) = [-1] + [-1]x3 + x2   
POL(LOAD1232(x1, x2, x3)) = [-1] + x3 + [-1]x2   
POL(&&(x1, x2)) = [-1]   
POL(<=(x1, x2)) = [-1]   
POL(COND_LOAD1222(x1, x2, x3, x4)) = [-1] + x4 + [-1]x3 + [-1]x1   
POL(>=(x1, x2)) = [-1]   
POL(0) = 0   
POL(>(x1, x2)) = [-1]   

The following pairs are in P>:

LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])

The following pairs are in Pbound:

COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3])
LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])
LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])

The following pairs are in P≥:

COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3])
LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])
COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[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

(32) Complex Obligation (AND)

(33) Obligation:

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


The following domains are used:

Boolean, Integer


R is empty.

The integer pair graph contains the following rules and edges:
(3): COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3])
(2): LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(i85[2] <= i69[2] && i79[2] <= i69[2], i79[2], i85[2], i69[2])
(1): COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1])

(1) -> (2), if ((i79[1] →* i79[2])∧(i69[1] →* i69[2])∧(i85[1] →* i85[2]))


(2) -> (3), if ((i85[2] →* i85[3])∧(i69[2] →* i69[3])∧(i85[2] <= i69[2] && i79[2] <= i69[2] →* TRUE)∧(i79[2] →* i79[3]))



The set Q consists of the following terms:
Load1222(x0, x1, x2)
Cond_Load1222(TRUE, x0, x1, x2)
Load1232(x0, x1, x2)
Cond_Load1232(TRUE, x0, x1, x2)
Cond_Load12221(TRUE, x0, x1, x2)
Cond_Load12321(TRUE, x0, x1, x2)
Cond_Load12222(TRUE, x0, x1, x2)
Cond_Load12322(TRUE, x0, x1, x2)
Cond_Load12223(TRUE, x0, x1, x2)

(34) IDependencyGraphProof (EQUIVALENT transformation)

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

(35) TRUE

(36) Obligation:

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


The following domains are used:
none


R is empty.

The integer pair graph contains the following rules and edges:
(1): COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1])


The set Q consists of the following terms:
Load1222(x0, x1, x2)
Cond_Load1222(TRUE, x0, x1, x2)
Load1232(x0, x1, x2)
Cond_Load1232(TRUE, x0, x1, x2)
Cond_Load12221(TRUE, x0, x1, x2)
Cond_Load12321(TRUE, x0, x1, x2)
Cond_Load12222(TRUE, x0, x1, x2)
Cond_Load12322(TRUE, x0, x1, x2)
Cond_Load12223(TRUE, x0, x1, x2)

(37) IDependencyGraphProof (EQUIVALENT transformation)

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

(38) TRUE

(39) 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:
(1): COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1])
(2): LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(i85[2] <= i69[2] && i79[2] <= i69[2], i79[2], i85[2], i69[2])
(3): COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3])
(10): LOAD1232(i79[10], i85[10], i69[10]) → COND_LOAD12322(i69[10] >= 0 && i79[10] > i69[10], i79[10], i85[10], i69[10])
(11): COND_LOAD12322(TRUE, i79[11], i85[11], i69[11]) → LOAD1222(i79[11] + -1, i85[11], i69[11])
(12): LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(i69[12] >= 0 && i79[12] > i69[12], i79[12], i85[12], i69[12])
(13): COND_LOAD12223(TRUE, i79[13], i85[13], i69[13]) → LOAD1222(i79[13] + -1, i85[13], i69[13])

(1) -> (2), if ((i79[1] →* i79[2])∧(i69[1] →* i69[2])∧(i85[1] →* i85[2]))


(2) -> (3), if ((i85[2] →* i85[3])∧(i69[2] →* i69[3])∧(i85[2] <= i69[2] && i79[2] <= i69[2] →* TRUE)∧(i79[2] →* i79[3]))


(1) -> (10), if ((i69[1] →* i69[10])∧(i79[1] →* i79[10])∧(i85[1] →* i85[10]))


(10) -> (11), if ((i85[10] →* i85[11])∧(i69[10] >= 0 && i79[10] > i69[10] →* TRUE)∧(i69[10] →* i69[11])∧(i79[10] →* i79[11]))


(3) -> (12), if ((i85[3] →* i85[12])∧(i69[3] →* i69[12])∧(i79[3] →* i79[12]))


(11) -> (12), if ((i79[11] + -1 →* i79[12])∧(i85[11] →* i85[12])∧(i69[11] →* i69[12]))


(13) -> (12), if ((i69[13] →* i69[12])∧(i85[13] →* i85[12])∧(i79[13] + -1 →* i79[12]))


(12) -> (13), if ((i85[12] →* i85[13])∧(i69[12] →* i69[13])∧(i79[12] →* i79[13])∧(i69[12] >= 0 && i79[12] > i69[12] →* TRUE))



The set Q consists of the following terms:
Load1222(x0, x1, x2)
Cond_Load1222(TRUE, x0, x1, x2)
Load1232(x0, x1, x2)
Cond_Load1232(TRUE, x0, x1, x2)
Cond_Load12221(TRUE, x0, x1, x2)
Cond_Load12321(TRUE, x0, x1, x2)
Cond_Load12222(TRUE, x0, x1, x2)
Cond_Load12322(TRUE, x0, x1, x2)
Cond_Load12223(TRUE, x0, x1, x2)

(40) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 5 less nodes.

(41) 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:
(13): COND_LOAD12223(TRUE, i79[13], i85[13], i69[13]) → LOAD1222(i79[13] + -1, i85[13], i69[13])
(12): LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(i69[12] >= 0 && i79[12] > i69[12], i79[12], i85[12], i69[12])

(13) -> (12), if ((i69[13] →* i69[12])∧(i85[13] →* i85[12])∧(i79[13] + -1 →* i79[12]))


(12) -> (13), if ((i85[12] →* i85[13])∧(i69[12] →* i69[13])∧(i79[12] →* i79[13])∧(i69[12] >= 0 && i79[12] > i69[12] →* TRUE))



The set Q consists of the following terms:
Load1222(x0, x1, x2)
Cond_Load1222(TRUE, x0, x1, x2)
Load1232(x0, x1, x2)
Cond_Load1232(TRUE, x0, x1, x2)
Cond_Load12221(TRUE, x0, x1, x2)
Cond_Load12321(TRUE, x0, x1, x2)
Cond_Load12222(TRUE, x0, x1, x2)
Cond_Load12322(TRUE, x0, x1, x2)
Cond_Load12223(TRUE, x0, x1, x2)

(42) IDPNonInfProof (SOUND transformation)

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


For Pair COND_LOAD12223(TRUE, i79[13], i85[13], i69[13]) → LOAD1222(+(i79[13], -1), i85[13], i69[13]) the following chains were created:
  • We consider the chain LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12]), COND_LOAD12223(TRUE, i79[13], i85[13], i69[13]) → LOAD1222(+(i79[13], -1), i85[13], i69[13]), LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12]) which results in the following constraint:

    (1)    (i85[12]=i85[13]∧i69[12]=i69[13]∧i79[12]=i79[13]∧&&(>=(i69[12], 0), >(i79[12], i69[12]))=TRUE∧i69[13]=i69[12]1∧i85[13]=i85[12]1∧+(i79[13], -1)=i79[12]1 ⇒ COND_LOAD12223(TRUE, i79[13], i85[13], i69[13])≥NonInfC∧COND_LOAD12223(TRUE, i79[13], i85[13], i69[13])≥LOAD1222(+(i79[13], -1), i85[13], i69[13])∧(UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥))



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

    (2)    (>=(i69[12], 0)=TRUE∧>(i79[12], i69[12])=TRUE ⇒ COND_LOAD12223(TRUE, i79[12], i85[12], i69[12])≥NonInfC∧COND_LOAD12223(TRUE, i79[12], i85[12], i69[12])≥LOAD1222(+(i79[12], -1), i85[12], i69[12])∧(UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥))



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

    (3)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧[(-1)bni_15 + (-1)Bound*bni_15] + [(-1)bni_15]i69[12] + [bni_15]i79[12] ≥ 0∧[1 + (-1)bso_16] ≥ 0)



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

    (4)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧[(-1)bni_15 + (-1)Bound*bni_15] + [(-1)bni_15]i69[12] + [bni_15]i79[12] ≥ 0∧[1 + (-1)bso_16] ≥ 0)



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

    (5)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧[(-1)bni_15 + (-1)Bound*bni_15] + [(-1)bni_15]i69[12] + [bni_15]i79[12] ≥ 0∧[1 + (-1)bso_16] ≥ 0)



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

    (6)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧0 = 0∧[(-1)bni_15 + (-1)Bound*bni_15] + [(-1)bni_15]i69[12] + [bni_15]i79[12] ≥ 0∧0 = 0∧[1 + (-1)bso_16] ≥ 0)



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

    (7)    (i69[12] ≥ 0∧i79[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧0 = 0∧[(-1)Bound*bni_15] + [bni_15]i79[12] ≥ 0∧0 = 0∧[1 + (-1)bso_16] ≥ 0)







For Pair LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12]) the following chains were created:
  • We consider the chain LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12]), COND_LOAD12223(TRUE, i79[13], i85[13], i69[13]) → LOAD1222(+(i79[13], -1), i85[13], i69[13]) which results in the following constraint:

    (8)    (i85[12]=i85[13]∧i69[12]=i69[13]∧i79[12]=i79[13]∧&&(>=(i69[12], 0), >(i79[12], i69[12]))=TRUE ⇒ LOAD1222(i79[12], i85[12], i69[12])≥NonInfC∧LOAD1222(i79[12], i85[12], i69[12])≥COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])∧(UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥))



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

    (9)    (>=(i69[12], 0)=TRUE∧>(i79[12], i69[12])=TRUE ⇒ LOAD1222(i79[12], i85[12], i69[12])≥NonInfC∧LOAD1222(i79[12], i85[12], i69[12])≥COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])∧(UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥))



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

    (10)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥)∧[(-1)bni_17 + (-1)Bound*bni_17] + [(-1)bni_17]i69[12] + [bni_17]i79[12] ≥ 0∧[(-1)bso_18] ≥ 0)



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

    (11)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥)∧[(-1)bni_17 + (-1)Bound*bni_17] + [(-1)bni_17]i69[12] + [bni_17]i79[12] ≥ 0∧[(-1)bso_18] ≥ 0)



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

    (12)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥)∧[(-1)bni_17 + (-1)Bound*bni_17] + [(-1)bni_17]i69[12] + [bni_17]i79[12] ≥ 0∧[(-1)bso_18] ≥ 0)



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

    (13)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥)∧0 = 0∧[(-1)bni_17 + (-1)Bound*bni_17] + [(-1)bni_17]i69[12] + [bni_17]i79[12] ≥ 0∧0 = 0∧[(-1)bso_18] ≥ 0)



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

    (14)    (i69[12] ≥ 0∧i79[12] ≥ 0 ⇒ (UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥)∧0 = 0∧[(-1)Bound*bni_17] + [bni_17]i79[12] ≥ 0∧0 = 0∧[(-1)bso_18] ≥ 0)







To summarize, we get the following constraints P≥ for the following pairs.
  • COND_LOAD12223(TRUE, i79[13], i85[13], i69[13]) → LOAD1222(+(i79[13], -1), i85[13], i69[13])
    • (i69[12] ≥ 0∧i79[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧0 = 0∧[(-1)Bound*bni_15] + [bni_15]i79[12] ≥ 0∧0 = 0∧[1 + (-1)bso_16] ≥ 0)

  • LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])
    • (i69[12] ≥ 0∧i79[12] ≥ 0 ⇒ (UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥)∧0 = 0∧[(-1)Bound*bni_17] + [bni_17]i79[12] ≥ 0∧0 = 0∧[(-1)bso_18] ≥ 0)




The constraints for P> respective Pbound are constructed from P≥ where we just replace every occurence of "t ≥ s" in P≥ by "t > s" respective "t ≥ c". Here c stands for the fresh constant used for Pbound.
Using the following integer polynomial ordering the resulting constraints can be solved
Polynomial interpretation over integers[POLO]:

POL(TRUE) = 0   
POL(FALSE) = 0   
POL(COND_LOAD12223(x1, x2, x3, x4)) = [-1] + [-1]x4 + x2 + [-1]x1   
POL(LOAD1222(x1, x2, x3)) = [-1] + [-1]x3 + x1   
POL(+(x1, x2)) = x1 + x2   
POL(-1) = [-1]   
POL(&&(x1, x2)) = 0   
POL(>=(x1, x2)) = [-1]   
POL(0) = 0   
POL(>(x1, x2)) = [-1]   

The following pairs are in P>:

COND_LOAD12223(TRUE, i79[13], i85[13], i69[13]) → LOAD1222(+(i79[13], -1), i85[13], i69[13])

The following pairs are in Pbound:

COND_LOAD12223(TRUE, i79[13], i85[13], i69[13]) → LOAD1222(+(i79[13], -1), i85[13], i69[13])
LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])

The following pairs are in P≥:

LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])

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

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

(43) Complex Obligation (AND)

(44) 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:
(12): LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(i69[12] >= 0 && i79[12] > i69[12], i79[12], i85[12], i69[12])


The set Q consists of the following terms:
Load1222(x0, x1, x2)
Cond_Load1222(TRUE, x0, x1, x2)
Load1232(x0, x1, x2)
Cond_Load1232(TRUE, x0, x1, x2)
Cond_Load12221(TRUE, x0, x1, x2)
Cond_Load12321(TRUE, x0, x1, x2)
Cond_Load12222(TRUE, x0, x1, x2)
Cond_Load12322(TRUE, x0, x1, x2)
Cond_Load12223(TRUE, x0, x1, x2)

(45) IDependencyGraphProof (EQUIVALENT transformation)

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

(46) TRUE

(47) Obligation:

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


The following domains are used:
none


R is empty.

The integer pair graph is empty.

The set Q consists of the following terms:
Load1222(x0, x1, x2)
Cond_Load1222(TRUE, x0, x1, x2)
Load1232(x0, x1, x2)
Cond_Load1232(TRUE, x0, x1, x2)
Cond_Load12221(TRUE, x0, x1, x2)
Cond_Load12321(TRUE, x0, x1, x2)
Cond_Load12222(TRUE, x0, x1, x2)
Cond_Load12322(TRUE, x0, x1, x2)
Cond_Load12223(TRUE, x0, x1, x2)

(48) IDependencyGraphProof (EQUIVALENT transformation)

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

(49) TRUE

(50) Obligation:

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


The following domains are used:

Boolean, Integer


R is empty.

The integer pair graph contains the following rules and edges:
(0): LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(i69[0] >= 0 && i85[0] > i69[0] && i79[0] <= i69[0], i79[0], i85[0], i69[0])
(1): COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1])
(2): LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(i85[2] <= i69[2] && i79[2] <= i69[2], i79[2], i85[2], i69[2])
(3): COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3])
(5): COND_LOAD12221(TRUE, i79[5], i85[5], i69[5]) → LOAD1222(i79[5], i85[5], i69[5])
(6): LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(i69[6] >= 0 && i85[6] > i69[6] && i79[6] <= i69[6], i79[6], i85[6], i69[6])
(7): COND_LOAD12321(TRUE, i79[7], i85[7], i69[7]) → LOAD1222(i79[7], i85[7] + -1, i69[7])
(10): LOAD1232(i79[10], i85[10], i69[10]) → COND_LOAD12322(i69[10] >= 0 && i79[10] > i69[10], i79[10], i85[10], i69[10])
(11): COND_LOAD12322(TRUE, i79[11], i85[11], i69[11]) → LOAD1222(i79[11] + -1, i85[11], i69[11])
(12): LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(i69[12] >= 0 && i79[12] > i69[12], i79[12], i85[12], i69[12])
(13): COND_LOAD12223(TRUE, i79[13], i85[13], i69[13]) → LOAD1222(i79[13] + -1, i85[13], i69[13])

(3) -> (0), if ((i79[3] →* i79[0])∧(i69[3] →* i69[0])∧(i85[3] →* i85[0]))


(5) -> (0), if ((i85[5] →* i85[0])∧(i69[5] →* i69[0])∧(i79[5] →* i79[0]))


(7) -> (0), if ((i85[7] + -1 →* i85[0])∧(i79[7] →* i79[0])∧(i69[7] →* i69[0]))


(11) -> (0), if ((i79[11] + -1 →* i79[0])∧(i85[11] →* i85[0])∧(i69[11] →* i69[0]))


(13) -> (0), if ((i69[13] →* i69[0])∧(i79[13] + -1 →* i79[0])∧(i85[13] →* i85[0]))


(0) -> (1), if ((i79[0] →* i79[1])∧(i85[0] →* i85[1])∧(i69[0] →* i69[1])∧(i69[0] >= 0 && i85[0] > i69[0] && i79[0] <= i69[0] →* TRUE))


(1) -> (2), if ((i79[1] →* i79[2])∧(i69[1] →* i69[2])∧(i85[1] →* i85[2]))


(2) -> (3), if ((i85[2] →* i85[3])∧(i69[2] →* i69[3])∧(i85[2] <= i69[2] && i79[2] <= i69[2] →* TRUE)∧(i79[2] →* i79[3]))


(1) -> (6), if ((i79[1] →* i79[6])∧(i85[1] →* i85[6])∧(i69[1] →* i69[6]))


(6) -> (7), if ((i85[6] →* i85[7])∧(i69[6] >= 0 && i85[6] > i69[6] && i79[6] <= i69[6] →* TRUE)∧(i69[6] →* i69[7])∧(i79[6] →* i79[7]))


(1) -> (10), if ((i69[1] →* i69[10])∧(i79[1] →* i79[10])∧(i85[1] →* i85[10]))


(10) -> (11), if ((i85[10] →* i85[11])∧(i69[10] >= 0 && i79[10] > i69[10] →* TRUE)∧(i69[10] →* i69[11])∧(i79[10] →* i79[11]))


(3) -> (12), if ((i85[3] →* i85[12])∧(i69[3] →* i69[12])∧(i79[3] →* i79[12]))


(5) -> (12), if ((i85[5] →* i85[12])∧(i69[5] →* i69[12])∧(i79[5] →* i79[12]))


(7) -> (12), if ((i79[7] →* i79[12])∧(i69[7] →* i69[12])∧(i85[7] + -1 →* i85[12]))


(11) -> (12), if ((i79[11] + -1 →* i79[12])∧(i85[11] →* i85[12])∧(i69[11] →* i69[12]))


(13) -> (12), if ((i69[13] →* i69[12])∧(i85[13] →* i85[12])∧(i79[13] + -1 →* i79[12]))


(12) -> (13), if ((i85[12] →* i85[13])∧(i69[12] →* i69[13])∧(i79[12] →* i79[13])∧(i69[12] >= 0 && i79[12] > i69[12] →* TRUE))



The set Q consists of the following terms:
Load1222(x0, x1, x2)
Cond_Load1222(TRUE, x0, x1, x2)
Load1232(x0, x1, x2)
Cond_Load1232(TRUE, x0, x1, x2)
Cond_Load12221(TRUE, x0, x1, x2)
Cond_Load12321(TRUE, x0, x1, x2)
Cond_Load12222(TRUE, x0, x1, x2)
Cond_Load12322(TRUE, x0, x1, x2)
Cond_Load12223(TRUE, x0, x1, x2)

(51) IDependencyGraphProof (EQUIVALENT transformation)

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

(52) 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:
(11): COND_LOAD12322(TRUE, i79[11], i85[11], i69[11]) → LOAD1222(i79[11] + -1, i85[11], i69[11])
(10): LOAD1232(i79[10], i85[10], i69[10]) → COND_LOAD12322(i69[10] >= 0 && i79[10] > i69[10], i79[10], i85[10], i69[10])
(7): COND_LOAD12321(TRUE, i79[7], i85[7], i69[7]) → LOAD1222(i79[7], i85[7] + -1, i69[7])
(6): LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(i69[6] >= 0 && i85[6] > i69[6] && i79[6] <= i69[6], i79[6], i85[6], i69[6])
(13): COND_LOAD12223(TRUE, i79[13], i85[13], i69[13]) → LOAD1222(i79[13] + -1, i85[13], i69[13])
(12): LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(i69[12] >= 0 && i79[12] > i69[12], i79[12], i85[12], i69[12])
(3): COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3])
(2): LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(i85[2] <= i69[2] && i79[2] <= i69[2], i79[2], i85[2], i69[2])
(1): COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1])
(0): LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(i69[0] >= 0 && i85[0] > i69[0] && i79[0] <= i69[0], i79[0], i85[0], i69[0])

(3) -> (0), if ((i79[3] →* i79[0])∧(i69[3] →* i69[0])∧(i85[3] →* i85[0]))


(7) -> (0), if ((i85[7] + -1 →* i85[0])∧(i79[7] →* i79[0])∧(i69[7] →* i69[0]))


(11) -> (0), if ((i79[11] + -1 →* i79[0])∧(i85[11] →* i85[0])∧(i69[11] →* i69[0]))


(13) -> (0), if ((i69[13] →* i69[0])∧(i79[13] + -1 →* i79[0])∧(i85[13] →* i85[0]))


(0) -> (1), if ((i79[0] →* i79[1])∧(i85[0] →* i85[1])∧(i69[0] →* i69[1])∧(i69[0] >= 0 && i85[0] > i69[0] && i79[0] <= i69[0] →* TRUE))


(1) -> (2), if ((i79[1] →* i79[2])∧(i69[1] →* i69[2])∧(i85[1] →* i85[2]))


(2) -> (3), if ((i85[2] →* i85[3])∧(i69[2] →* i69[3])∧(i85[2] <= i69[2] && i79[2] <= i69[2] →* TRUE)∧(i79[2] →* i79[3]))


(1) -> (6), if ((i79[1] →* i79[6])∧(i85[1] →* i85[6])∧(i69[1] →* i69[6]))


(6) -> (7), if ((i85[6] →* i85[7])∧(i69[6] >= 0 && i85[6] > i69[6] && i79[6] <= i69[6] →* TRUE)∧(i69[6] →* i69[7])∧(i79[6] →* i79[7]))


(1) -> (10), if ((i69[1] →* i69[10])∧(i79[1] →* i79[10])∧(i85[1] →* i85[10]))


(10) -> (11), if ((i85[10] →* i85[11])∧(i69[10] >= 0 && i79[10] > i69[10] →* TRUE)∧(i69[10] →* i69[11])∧(i79[10] →* i79[11]))


(3) -> (12), if ((i85[3] →* i85[12])∧(i69[3] →* i69[12])∧(i79[3] →* i79[12]))


(7) -> (12), if ((i79[7] →* i79[12])∧(i69[7] →* i69[12])∧(i85[7] + -1 →* i85[12]))


(11) -> (12), if ((i79[11] + -1 →* i79[12])∧(i85[11] →* i85[12])∧(i69[11] →* i69[12]))


(13) -> (12), if ((i69[13] →* i69[12])∧(i85[13] →* i85[12])∧(i79[13] + -1 →* i79[12]))


(12) -> (13), if ((i85[12] →* i85[13])∧(i69[12] →* i69[13])∧(i79[12] →* i79[13])∧(i69[12] >= 0 && i79[12] > i69[12] →* TRUE))



The set Q consists of the following terms:
Load1222(x0, x1, x2)
Cond_Load1222(TRUE, x0, x1, x2)
Load1232(x0, x1, x2)
Cond_Load1232(TRUE, x0, x1, x2)
Cond_Load12221(TRUE, x0, x1, x2)
Cond_Load12321(TRUE, x0, x1, x2)
Cond_Load12222(TRUE, x0, x1, x2)
Cond_Load12322(TRUE, x0, x1, x2)
Cond_Load12223(TRUE, x0, x1, x2)

(53) IDPNonInfProof (SOUND transformation)

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


For Pair COND_LOAD12322(TRUE, i79[11], i85[11], i69[11]) → LOAD1222(+(i79[11], -1), i85[11], i69[11]) the following chains were created:
  • We consider the chain LOAD1232(i79[10], i85[10], i69[10]) → COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10]), COND_LOAD12322(TRUE, i79[11], i85[11], i69[11]) → LOAD1222(+(i79[11], -1), i85[11], i69[11]), LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]) which results in the following constraint:

    (1)    (i85[10]=i85[11]∧&&(>=(i69[10], 0), >(i79[10], i69[10]))=TRUE∧i69[10]=i69[11]∧i79[10]=i79[11]∧+(i79[11], -1)=i79[0]∧i85[11]=i85[0]∧i69[11]=i69[0] ⇒ COND_LOAD12322(TRUE, i79[11], i85[11], i69[11])≥NonInfC∧COND_LOAD12322(TRUE, i79[11], i85[11], i69[11])≥LOAD1222(+(i79[11], -1), i85[11], i69[11])∧(UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥))



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

    (2)    (>=(i69[10], 0)=TRUE∧>(i79[10], i69[10])=TRUE ⇒ COND_LOAD12322(TRUE, i79[10], i85[10], i69[10])≥NonInfC∧COND_LOAD12322(TRUE, i79[10], i85[10], i69[10])≥LOAD1222(+(i79[10], -1), i85[10], i69[10])∧(UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥))



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

    (3)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧[(-1)bni_40 + (-1)Bound*bni_40] + [(-1)bni_40]i69[10] + [bni_40]i79[10] ≥ 0∧[(-1)bso_41] ≥ 0)



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

    (4)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧[(-1)bni_40 + (-1)Bound*bni_40] + [(-1)bni_40]i69[10] + [bni_40]i79[10] ≥ 0∧[(-1)bso_41] ≥ 0)



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

    (5)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧[(-1)bni_40 + (-1)Bound*bni_40] + [(-1)bni_40]i69[10] + [bni_40]i79[10] ≥ 0∧[(-1)bso_41] ≥ 0)



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

    (6)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧0 = 0∧[(-1)bni_40 + (-1)Bound*bni_40] + [(-1)bni_40]i69[10] + [bni_40]i79[10] ≥ 0∧0 = 0∧[(-1)bso_41] ≥ 0)



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

    (7)    (i69[10] ≥ 0∧i79[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧0 = 0∧[(-1)Bound*bni_40] + [bni_40]i79[10] ≥ 0∧0 = 0∧[(-1)bso_41] ≥ 0)



  • We consider the chain LOAD1232(i79[10], i85[10], i69[10]) → COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10]), COND_LOAD12322(TRUE, i79[11], i85[11], i69[11]) → LOAD1222(+(i79[11], -1), i85[11], i69[11]), LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12]) which results in the following constraint:

    (8)    (i85[10]=i85[11]∧&&(>=(i69[10], 0), >(i79[10], i69[10]))=TRUE∧i69[10]=i69[11]∧i79[10]=i79[11]∧+(i79[11], -1)=i79[12]∧i85[11]=i85[12]∧i69[11]=i69[12] ⇒ COND_LOAD12322(TRUE, i79[11], i85[11], i69[11])≥NonInfC∧COND_LOAD12322(TRUE, i79[11], i85[11], i69[11])≥LOAD1222(+(i79[11], -1), i85[11], i69[11])∧(UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥))



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

    (9)    (>=(i69[10], 0)=TRUE∧>(i79[10], i69[10])=TRUE ⇒ COND_LOAD12322(TRUE, i79[10], i85[10], i69[10])≥NonInfC∧COND_LOAD12322(TRUE, i79[10], i85[10], i69[10])≥LOAD1222(+(i79[10], -1), i85[10], i69[10])∧(UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥))



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

    (10)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧[(-1)bni_40 + (-1)Bound*bni_40] + [(-1)bni_40]i69[10] + [bni_40]i79[10] ≥ 0∧[(-1)bso_41] ≥ 0)



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

    (11)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧[(-1)bni_40 + (-1)Bound*bni_40] + [(-1)bni_40]i69[10] + [bni_40]i79[10] ≥ 0∧[(-1)bso_41] ≥ 0)



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

    (12)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧[(-1)bni_40 + (-1)Bound*bni_40] + [(-1)bni_40]i69[10] + [bni_40]i79[10] ≥ 0∧[(-1)bso_41] ≥ 0)



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

    (13)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧0 = 0∧[(-1)bni_40 + (-1)Bound*bni_40] + [(-1)bni_40]i69[10] + [bni_40]i79[10] ≥ 0∧0 = 0∧[(-1)bso_41] ≥ 0)



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

    (14)    (i69[10] ≥ 0∧i79[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧0 = 0∧[(-1)Bound*bni_40] + [bni_40]i79[10] ≥ 0∧0 = 0∧[(-1)bso_41] ≥ 0)







For Pair LOAD1232(i79[10], i85[10], i69[10]) → COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10]) the following chains were created:
  • We consider the chain LOAD1232(i79[10], i85[10], i69[10]) → COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10]), COND_LOAD12322(TRUE, i79[11], i85[11], i69[11]) → LOAD1222(+(i79[11], -1), i85[11], i69[11]) which results in the following constraint:

    (15)    (i85[10]=i85[11]∧&&(>=(i69[10], 0), >(i79[10], i69[10]))=TRUE∧i69[10]=i69[11]∧i79[10]=i79[11] ⇒ LOAD1232(i79[10], i85[10], i69[10])≥NonInfC∧LOAD1232(i79[10], i85[10], i69[10])≥COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])∧(UIncreasing(COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])), ≥))



    We simplified constraint (15) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (16)    (>=(i69[10], 0)=TRUE∧>(i79[10], i69[10])=TRUE ⇒ LOAD1232(i79[10], i85[10], i69[10])≥NonInfC∧LOAD1232(i79[10], i85[10], i69[10])≥COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])∧(UIncreasing(COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])), ≥))



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

    (17)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])), ≥)∧[(-1)Bound*bni_42] + [(-1)bni_42]i69[10] + [bni_42]i79[10] ≥ 0∧[1 + (-1)bso_43] ≥ 0)



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

    (18)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])), ≥)∧[(-1)Bound*bni_42] + [(-1)bni_42]i69[10] + [bni_42]i79[10] ≥ 0∧[1 + (-1)bso_43] ≥ 0)



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

    (19)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])), ≥)∧[(-1)Bound*bni_42] + [(-1)bni_42]i69[10] + [bni_42]i79[10] ≥ 0∧[1 + (-1)bso_43] ≥ 0)



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

    (20)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])), ≥)∧0 = 0∧[(-1)Bound*bni_42] + [(-1)bni_42]i69[10] + [bni_42]i79[10] ≥ 0∧0 = 0∧[1 + (-1)bso_43] ≥ 0)



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

    (21)    (i69[10] ≥ 0∧i79[10] ≥ 0 ⇒ (UIncreasing(COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])), ≥)∧0 = 0∧[(-1)Bound*bni_42 + bni_42] + [bni_42]i79[10] ≥ 0∧0 = 0∧[1 + (-1)bso_43] ≥ 0)







For Pair COND_LOAD12321(TRUE, i79[7], i85[7], i69[7]) → LOAD1222(i79[7], +(i85[7], -1), i69[7]) the following chains were created:
  • We consider the chain LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6]), COND_LOAD12321(TRUE, i79[7], i85[7], i69[7]) → LOAD1222(i79[7], +(i85[7], -1), i69[7]), LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]) which results in the following constraint:

    (22)    (i85[6]=i85[7]∧&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6]))=TRUE∧i69[6]=i69[7]∧i79[6]=i79[7]∧+(i85[7], -1)=i85[0]∧i79[7]=i79[0]∧i69[7]=i69[0] ⇒ COND_LOAD12321(TRUE, i79[7], i85[7], i69[7])≥NonInfC∧COND_LOAD12321(TRUE, i79[7], i85[7], i69[7])≥LOAD1222(i79[7], +(i85[7], -1), i69[7])∧(UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥))



    We simplified constraint (22) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (23)    (<=(i79[6], i69[6])=TRUE∧>=(i69[6], 0)=TRUE∧>(i85[6], i69[6])=TRUE ⇒ COND_LOAD12321(TRUE, i79[6], i85[6], i69[6])≥NonInfC∧COND_LOAD12321(TRUE, i79[6], i85[6], i69[6])≥LOAD1222(i79[6], +(i85[6], -1), i69[6])∧(UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥))



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

    (24)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] + [-1] + [-1]i69[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_44] + [(-1)bni_44]i69[6] + [bni_44]i79[6] ≥ 0∧[(-1)bso_45] ≥ 0)



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

    (25)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] + [-1] + [-1]i69[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_44] + [(-1)bni_44]i69[6] + [bni_44]i79[6] ≥ 0∧[(-1)bso_45] ≥ 0)



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

    (26)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] + [-1] + [-1]i69[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_44] + [(-1)bni_44]i69[6] + [bni_44]i79[6] ≥ 0∧[(-1)bso_45] ≥ 0)



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

    (27)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_44] + [(-1)bni_44]i69[6] + [bni_44]i79[6] ≥ 0∧[(-1)bso_45] ≥ 0)



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

    (28)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_44] + [(-1)bni_44]i69[6] + [bni_44]i79[6] ≥ 0∧[(-1)bso_45] ≥ 0)


    (29)    (i69[6] + i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_44] + [(-1)bni_44]i69[6] + [(-1)bni_44]i79[6] ≥ 0∧[(-1)bso_45] ≥ 0)



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

    (30)    (i69[6] ≥ 0∧i79[6] + i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_44] + [(-1)bni_44]i69[6] ≥ 0∧[(-1)bso_45] ≥ 0)



  • We consider the chain LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6]), COND_LOAD12321(TRUE, i79[7], i85[7], i69[7]) → LOAD1222(i79[7], +(i85[7], -1), i69[7]), LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12]) which results in the following constraint:

    (31)    (i85[6]=i85[7]∧&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6]))=TRUE∧i69[6]=i69[7]∧i79[6]=i79[7]∧i79[7]=i79[12]∧i69[7]=i69[12]∧+(i85[7], -1)=i85[12] ⇒ COND_LOAD12321(TRUE, i79[7], i85[7], i69[7])≥NonInfC∧COND_LOAD12321(TRUE, i79[7], i85[7], i69[7])≥LOAD1222(i79[7], +(i85[7], -1), i69[7])∧(UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥))



    We simplified constraint (31) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (32)    (<=(i79[6], i69[6])=TRUE∧>=(i69[6], 0)=TRUE∧>(i85[6], i69[6])=TRUE ⇒ COND_LOAD12321(TRUE, i79[6], i85[6], i69[6])≥NonInfC∧COND_LOAD12321(TRUE, i79[6], i85[6], i69[6])≥LOAD1222(i79[6], +(i85[6], -1), i69[6])∧(UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥))



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

    (33)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] + [-1] + [-1]i69[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_44] + [(-1)bni_44]i69[6] + [bni_44]i79[6] ≥ 0∧[(-1)bso_45] ≥ 0)



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

    (34)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] + [-1] + [-1]i69[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_44] + [(-1)bni_44]i69[6] + [bni_44]i79[6] ≥ 0∧[(-1)bso_45] ≥ 0)



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

    (35)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] + [-1] + [-1]i69[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_44] + [(-1)bni_44]i69[6] + [bni_44]i79[6] ≥ 0∧[(-1)bso_45] ≥ 0)



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

    (36)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_44] + [(-1)bni_44]i69[6] + [bni_44]i79[6] ≥ 0∧[(-1)bso_45] ≥ 0)



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

    (37)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_44] + [(-1)bni_44]i69[6] + [bni_44]i79[6] ≥ 0∧[(-1)bso_45] ≥ 0)


    (38)    (i69[6] + i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_44] + [(-1)bni_44]i69[6] + [(-1)bni_44]i79[6] ≥ 0∧[(-1)bso_45] ≥ 0)



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

    (39)    (i69[6] ≥ 0∧i79[6] + i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_44] + [(-1)bni_44]i69[6] ≥ 0∧[(-1)bso_45] ≥ 0)







For Pair LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6]) the following chains were created:
  • We consider the chain LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6]), COND_LOAD12321(TRUE, i79[7], i85[7], i69[7]) → LOAD1222(i79[7], +(i85[7], -1), i69[7]) which results in the following constraint:

    (40)    (i85[6]=i85[7]∧&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6]))=TRUE∧i69[6]=i69[7]∧i79[6]=i79[7] ⇒ LOAD1232(i79[6], i85[6], i69[6])≥NonInfC∧LOAD1232(i79[6], i85[6], i69[6])≥COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])∧(UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥))



    We simplified constraint (40) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (41)    (<=(i79[6], i69[6])=TRUE∧>=(i69[6], 0)=TRUE∧>(i85[6], i69[6])=TRUE ⇒ LOAD1232(i79[6], i85[6], i69[6])≥NonInfC∧LOAD1232(i79[6], i85[6], i69[6])≥COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])∧(UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥))



    We simplified constraint (41) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (42)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] + [-1] + [-1]i69[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)Bound*bni_46] + [(-1)bni_46]i69[6] + [bni_46]i79[6] ≥ 0∧[(-1)bso_47] ≥ 0)



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

    (43)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] + [-1] + [-1]i69[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)Bound*bni_46] + [(-1)bni_46]i69[6] + [bni_46]i79[6] ≥ 0∧[(-1)bso_47] ≥ 0)



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

    (44)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] + [-1] + [-1]i69[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)Bound*bni_46] + [(-1)bni_46]i69[6] + [bni_46]i79[6] ≥ 0∧[(-1)bso_47] ≥ 0)



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

    (45)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)Bound*bni_46] + [(-1)bni_46]i69[6] + [bni_46]i79[6] ≥ 0∧[(-1)bso_47] ≥ 0)



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

    (46)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)Bound*bni_46] + [(-1)bni_46]i69[6] + [bni_46]i79[6] ≥ 0∧[(-1)bso_47] ≥ 0)


    (47)    (i69[6] + i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)Bound*bni_46] + [(-1)bni_46]i69[6] + [(-1)bni_46]i79[6] ≥ 0∧[(-1)bso_47] ≥ 0)



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

    (48)    (i69[6] ≥ 0∧i79[6] + i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)Bound*bni_46] + [(-1)bni_46]i69[6] ≥ 0∧[(-1)bso_47] ≥ 0)







For Pair COND_LOAD12223(TRUE, i79[13], i85[13], i69[13]) → LOAD1222(+(i79[13], -1), i85[13], i69[13]) the following chains were created:
  • We consider the chain LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12]), COND_LOAD12223(TRUE, i79[13], i85[13], i69[13]) → LOAD1222(+(i79[13], -1), i85[13], i69[13]), LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]) which results in the following constraint:

    (49)    (i85[12]=i85[13]∧i69[12]=i69[13]∧i79[12]=i79[13]∧&&(>=(i69[12], 0), >(i79[12], i69[12]))=TRUE∧i69[13]=i69[0]∧+(i79[13], -1)=i79[0]∧i85[13]=i85[0] ⇒ COND_LOAD12223(TRUE, i79[13], i85[13], i69[13])≥NonInfC∧COND_LOAD12223(TRUE, i79[13], i85[13], i69[13])≥LOAD1222(+(i79[13], -1), i85[13], i69[13])∧(UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥))



    We simplified constraint (49) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (50)    (>=(i69[12], 0)=TRUE∧>(i79[12], i69[12])=TRUE ⇒ COND_LOAD12223(TRUE, i79[12], i85[12], i69[12])≥NonInfC∧COND_LOAD12223(TRUE, i79[12], i85[12], i69[12])≥LOAD1222(+(i79[12], -1), i85[12], i69[12])∧(UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥))



    We simplified constraint (50) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (51)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧[(-1)bni_48 + (-1)Bound*bni_48] + [(-1)bni_48]i69[12] + [bni_48]i79[12] ≥ 0∧[(-1)bso_49] ≥ 0)



    We simplified constraint (51) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (52)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧[(-1)bni_48 + (-1)Bound*bni_48] + [(-1)bni_48]i69[12] + [bni_48]i79[12] ≥ 0∧[(-1)bso_49] ≥ 0)



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

    (53)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧[(-1)bni_48 + (-1)Bound*bni_48] + [(-1)bni_48]i69[12] + [bni_48]i79[12] ≥ 0∧[(-1)bso_49] ≥ 0)



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

    (54)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧0 = 0∧[(-1)bni_48 + (-1)Bound*bni_48] + [(-1)bni_48]i69[12] + [bni_48]i79[12] ≥ 0∧0 = 0∧[(-1)bso_49] ≥ 0)



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

    (55)    (i69[12] ≥ 0∧i79[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧0 = 0∧[(-1)Bound*bni_48] + [bni_48]i79[12] ≥ 0∧0 = 0∧[(-1)bso_49] ≥ 0)



  • We consider the chain LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12]), COND_LOAD12223(TRUE, i79[13], i85[13], i69[13]) → LOAD1222(+(i79[13], -1), i85[13], i69[13]), LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12]) which results in the following constraint:

    (56)    (i85[12]=i85[13]∧i69[12]=i69[13]∧i79[12]=i79[13]∧&&(>=(i69[12], 0), >(i79[12], i69[12]))=TRUE∧i69[13]=i69[12]1∧i85[13]=i85[12]1∧+(i79[13], -1)=i79[12]1 ⇒ COND_LOAD12223(TRUE, i79[13], i85[13], i69[13])≥NonInfC∧COND_LOAD12223(TRUE, i79[13], i85[13], i69[13])≥LOAD1222(+(i79[13], -1), i85[13], i69[13])∧(UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥))



    We simplified constraint (56) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (57)    (>=(i69[12], 0)=TRUE∧>(i79[12], i69[12])=TRUE ⇒ COND_LOAD12223(TRUE, i79[12], i85[12], i69[12])≥NonInfC∧COND_LOAD12223(TRUE, i79[12], i85[12], i69[12])≥LOAD1222(+(i79[12], -1), i85[12], i69[12])∧(UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥))



    We simplified constraint (57) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (58)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧[(-1)bni_48 + (-1)Bound*bni_48] + [(-1)bni_48]i69[12] + [bni_48]i79[12] ≥ 0∧[(-1)bso_49] ≥ 0)



    We simplified constraint (58) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (59)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧[(-1)bni_48 + (-1)Bound*bni_48] + [(-1)bni_48]i69[12] + [bni_48]i79[12] ≥ 0∧[(-1)bso_49] ≥ 0)



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

    (60)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧[(-1)bni_48 + (-1)Bound*bni_48] + [(-1)bni_48]i69[12] + [bni_48]i79[12] ≥ 0∧[(-1)bso_49] ≥ 0)



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

    (61)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧0 = 0∧[(-1)bni_48 + (-1)Bound*bni_48] + [(-1)bni_48]i69[12] + [bni_48]i79[12] ≥ 0∧0 = 0∧[(-1)bso_49] ≥ 0)



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

    (62)    (i69[12] ≥ 0∧i79[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧0 = 0∧[(-1)Bound*bni_48] + [bni_48]i79[12] ≥ 0∧0 = 0∧[(-1)bso_49] ≥ 0)







For Pair LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12]) the following chains were created:
  • We consider the chain LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12]), COND_LOAD12223(TRUE, i79[13], i85[13], i69[13]) → LOAD1222(+(i79[13], -1), i85[13], i69[13]) which results in the following constraint:

    (63)    (i85[12]=i85[13]∧i69[12]=i69[13]∧i79[12]=i79[13]∧&&(>=(i69[12], 0), >(i79[12], i69[12]))=TRUE ⇒ LOAD1222(i79[12], i85[12], i69[12])≥NonInfC∧LOAD1222(i79[12], i85[12], i69[12])≥COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])∧(UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥))



    We simplified constraint (63) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (64)    (>=(i69[12], 0)=TRUE∧>(i79[12], i69[12])=TRUE ⇒ LOAD1222(i79[12], i85[12], i69[12])≥NonInfC∧LOAD1222(i79[12], i85[12], i69[12])≥COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])∧(UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥))



    We simplified constraint (64) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (65)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥)∧[(-1)Bound*bni_50] + [(-1)bni_50]i69[12] + [bni_50]i79[12] ≥ 0∧[1 + (-1)bso_51] ≥ 0)



    We simplified constraint (65) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (66)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥)∧[(-1)Bound*bni_50] + [(-1)bni_50]i69[12] + [bni_50]i79[12] ≥ 0∧[1 + (-1)bso_51] ≥ 0)



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

    (67)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥)∧[(-1)Bound*bni_50] + [(-1)bni_50]i69[12] + [bni_50]i79[12] ≥ 0∧[1 + (-1)bso_51] ≥ 0)



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

    (68)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥)∧0 = 0∧[(-1)Bound*bni_50] + [(-1)bni_50]i69[12] + [bni_50]i79[12] ≥ 0∧0 = 0∧[1 + (-1)bso_51] ≥ 0)



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

    (69)    (i69[12] ≥ 0∧i79[12] ≥ 0 ⇒ (UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥)∧0 = 0∧[(-1)Bound*bni_50 + bni_50] + [bni_50]i79[12] ≥ 0∧0 = 0∧[1 + (-1)bso_51] ≥ 0)







For Pair COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3]) the following chains were created:
  • We consider the chain COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3]), LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]) which results in the following constraint:

    (70)    (i79[3]=i79[0]∧i69[3]=i69[0]∧i85[3]=i85[0] ⇒ COND_LOAD1232(TRUE, i79[3], i85[3], i69[3])≥NonInfC∧COND_LOAD1232(TRUE, i79[3], i85[3], i69[3])≥LOAD1222(i79[3], i85[3], i69[3])∧(UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥))



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

    (71)    (COND_LOAD1232(TRUE, i79[3], i85[3], i69[3])≥NonInfC∧COND_LOAD1232(TRUE, i79[3], i85[3], i69[3])≥LOAD1222(i79[3], i85[3], i69[3])∧(UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥))



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

    (72)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bso_53] ≥ 0)



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

    (73)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bso_53] ≥ 0)



    We simplified constraint (73) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (74)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bso_53] ≥ 0)



    We simplified constraint (74) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

    (75)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_53] ≥ 0)



  • We consider the chain COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3]), LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12]) which results in the following constraint:

    (76)    (i85[3]=i85[12]∧i69[3]=i69[12]∧i79[3]=i79[12] ⇒ COND_LOAD1232(TRUE, i79[3], i85[3], i69[3])≥NonInfC∧COND_LOAD1232(TRUE, i79[3], i85[3], i69[3])≥LOAD1222(i79[3], i85[3], i69[3])∧(UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥))



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

    (77)    (COND_LOAD1232(TRUE, i79[3], i85[3], i69[3])≥NonInfC∧COND_LOAD1232(TRUE, i79[3], i85[3], i69[3])≥LOAD1222(i79[3], i85[3], i69[3])∧(UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥))



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

    (78)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bso_53] ≥ 0)



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

    (79)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bso_53] ≥ 0)



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

    (80)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bso_53] ≥ 0)



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

    (81)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_53] ≥ 0)







For Pair LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2]) the following chains were created:
  • We consider the chain LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2]), COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3]) which results in the following constraint:

    (82)    (i85[2]=i85[3]∧i69[2]=i69[3]∧&&(<=(i85[2], i69[2]), <=(i79[2], i69[2]))=TRUE∧i79[2]=i79[3] ⇒ LOAD1232(i79[2], i85[2], i69[2])≥NonInfC∧LOAD1232(i79[2], i85[2], i69[2])≥COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])∧(UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥))



    We simplified constraint (82) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (83)    (<=(i85[2], i69[2])=TRUE∧<=(i79[2], i69[2])=TRUE ⇒ LOAD1232(i79[2], i85[2], i69[2])≥NonInfC∧LOAD1232(i79[2], i85[2], i69[2])≥COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])∧(UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥))



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

    (84)    (i69[2] + [-1]i85[2] ≥ 0∧i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)Bound*bni_54] + [(-1)bni_54]i69[2] + [bni_54]i79[2] ≥ 0∧[(-1)bso_55] ≥ 0)



    We simplified constraint (84) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (85)    (i69[2] + [-1]i85[2] ≥ 0∧i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)Bound*bni_54] + [(-1)bni_54]i69[2] + [bni_54]i79[2] ≥ 0∧[(-1)bso_55] ≥ 0)



    We simplified constraint (85) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (86)    (i69[2] + [-1]i85[2] ≥ 0∧i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)Bound*bni_54] + [(-1)bni_54]i69[2] + [bni_54]i79[2] ≥ 0∧[(-1)bso_55] ≥ 0)



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

    (87)    (i69[2] ≥ 0∧i85[2] + i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)Bound*bni_54] + [(-1)bni_54]i85[2] + [(-1)bni_54]i69[2] + [bni_54]i79[2] ≥ 0∧[(-1)bso_55] ≥ 0)



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

    (88)    (i69[2] ≥ 0∧i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)Bound*bni_54] + [(-1)bni_54]i79[2] ≥ 0∧[(-1)bso_55] ≥ 0)



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

    (89)    (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)Bound*bni_54] + [(-1)bni_54]i79[2] ≥ 0∧[(-1)bso_55] ≥ 0)


    (90)    (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)Bound*bni_54] + [(-1)bni_54]i79[2] ≥ 0∧[(-1)bso_55] ≥ 0)







For Pair COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1]) the following chains were created:
  • We consider the chain COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1]), LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2]) which results in the following constraint:

    (91)    (i79[1]=i79[2]∧i69[1]=i69[2]∧i85[1]=i85[2] ⇒ COND_LOAD1222(TRUE, i79[1], i85[1], i69[1])≥NonInfC∧COND_LOAD1222(TRUE, i79[1], i85[1], i69[1])≥LOAD1232(i79[1], i85[1], i69[1])∧(UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥))



    We simplified constraint (91) using rule (IV) which results in the following new constraint:

    (92)    (COND_LOAD1222(TRUE, i79[1], i85[1], i69[1])≥NonInfC∧COND_LOAD1222(TRUE, i79[1], i85[1], i69[1])≥LOAD1232(i79[1], i85[1], i69[1])∧(UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥))



    We simplified constraint (92) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (93)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_57] ≥ 0)



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

    (94)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_57] ≥ 0)



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

    (95)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_57] ≥ 0)



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

    (96)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_57] ≥ 0)



  • We consider the chain COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1]), LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6]) which results in the following constraint:

    (97)    (i79[1]=i79[6]∧i85[1]=i85[6]∧i69[1]=i69[6] ⇒ COND_LOAD1222(TRUE, i79[1], i85[1], i69[1])≥NonInfC∧COND_LOAD1222(TRUE, i79[1], i85[1], i69[1])≥LOAD1232(i79[1], i85[1], i69[1])∧(UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥))



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

    (98)    (COND_LOAD1222(TRUE, i79[1], i85[1], i69[1])≥NonInfC∧COND_LOAD1222(TRUE, i79[1], i85[1], i69[1])≥LOAD1232(i79[1], i85[1], i69[1])∧(UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥))



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

    (99)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_57] ≥ 0)



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

    (100)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_57] ≥ 0)



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

    (101)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_57] ≥ 0)



    We simplified constraint (101) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

    (102)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_57] ≥ 0)



  • We consider the chain COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1]), LOAD1232(i79[10], i85[10], i69[10]) → COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10]) which results in the following constraint:

    (103)    (i69[1]=i69[10]∧i79[1]=i79[10]∧i85[1]=i85[10] ⇒ COND_LOAD1222(TRUE, i79[1], i85[1], i69[1])≥NonInfC∧COND_LOAD1222(TRUE, i79[1], i85[1], i69[1])≥LOAD1232(i79[1], i85[1], i69[1])∧(UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥))



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

    (104)    (COND_LOAD1222(TRUE, i79[1], i85[1], i69[1])≥NonInfC∧COND_LOAD1222(TRUE, i79[1], i85[1], i69[1])≥LOAD1232(i79[1], i85[1], i69[1])∧(UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥))



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

    (105)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_57] ≥ 0)



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

    (106)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_57] ≥ 0)



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

    (107)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_57] ≥ 0)



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

    (108)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_57] ≥ 0)







For Pair LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]) the following chains were created:
  • We consider the chain LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]), COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1]) which results in the following constraint:

    (109)    (i79[0]=i79[1]∧i85[0]=i85[1]∧i69[0]=i69[1]∧&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0]))=TRUE ⇒ LOAD1222(i79[0], i85[0], i69[0])≥NonInfC∧LOAD1222(i79[0], i85[0], i69[0])≥COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])∧(UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥))



    We simplified constraint (109) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (110)    (<=(i79[0], i69[0])=TRUE∧>=(i69[0], 0)=TRUE∧>(i85[0], i69[0])=TRUE ⇒ LOAD1222(i79[0], i85[0], i69[0])≥NonInfC∧LOAD1222(i79[0], i85[0], i69[0])≥COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])∧(UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥))



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

    (111)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] + [-1] + [-1]i69[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_58] + [(-1)bni_58]i69[0] + [bni_58]i79[0] ≥ 0∧[(-1)bso_59] ≥ 0)



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

    (112)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] + [-1] + [-1]i69[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_58] + [(-1)bni_58]i69[0] + [bni_58]i79[0] ≥ 0∧[(-1)bso_59] ≥ 0)



    We simplified constraint (112) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (113)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] + [-1] + [-1]i69[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_58] + [(-1)bni_58]i69[0] + [bni_58]i79[0] ≥ 0∧[(-1)bso_59] ≥ 0)



    We simplified constraint (113) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (114)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_58] + [(-1)bni_58]i69[0] + [bni_58]i79[0] ≥ 0∧[(-1)bso_59] ≥ 0)



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

    (115)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_58] + [(-1)bni_58]i69[0] + [bni_58]i79[0] ≥ 0∧[(-1)bso_59] ≥ 0)


    (116)    (i69[0] + i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_58] + [(-1)bni_58]i69[0] + [(-1)bni_58]i79[0] ≥ 0∧[(-1)bso_59] ≥ 0)



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

    (117)    (i69[0] ≥ 0∧i79[0] + i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_58] + [(-1)bni_58]i69[0] ≥ 0∧[(-1)bso_59] ≥ 0)







To summarize, we get the following constraints P≥ for the following pairs.
  • COND_LOAD12322(TRUE, i79[11], i85[11], i69[11]) → LOAD1222(+(i79[11], -1), i85[11], i69[11])
    • (i69[10] ≥ 0∧i79[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧0 = 0∧[(-1)Bound*bni_40] + [bni_40]i79[10] ≥ 0∧0 = 0∧[(-1)bso_41] ≥ 0)
    • (i69[10] ≥ 0∧i79[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧0 = 0∧[(-1)Bound*bni_40] + [bni_40]i79[10] ≥ 0∧0 = 0∧[(-1)bso_41] ≥ 0)

  • LOAD1232(i79[10], i85[10], i69[10]) → COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])
    • (i69[10] ≥ 0∧i79[10] ≥ 0 ⇒ (UIncreasing(COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])), ≥)∧0 = 0∧[(-1)Bound*bni_42 + bni_42] + [bni_42]i79[10] ≥ 0∧0 = 0∧[1 + (-1)bso_43] ≥ 0)

  • COND_LOAD12321(TRUE, i79[7], i85[7], i69[7]) → LOAD1222(i79[7], +(i85[7], -1), i69[7])
    • (i69[6] + i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_44] + [(-1)bni_44]i69[6] + [(-1)bni_44]i79[6] ≥ 0∧[(-1)bso_45] ≥ 0)
    • (i69[6] ≥ 0∧i79[6] + i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_44] + [(-1)bni_44]i69[6] ≥ 0∧[(-1)bso_45] ≥ 0)
    • (i69[6] + i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_44] + [(-1)bni_44]i69[6] + [(-1)bni_44]i79[6] ≥ 0∧[(-1)bso_45] ≥ 0)
    • (i69[6] ≥ 0∧i79[6] + i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_44] + [(-1)bni_44]i69[6] ≥ 0∧[(-1)bso_45] ≥ 0)

  • LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])
    • (i69[6] + i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)Bound*bni_46] + [(-1)bni_46]i69[6] + [(-1)bni_46]i79[6] ≥ 0∧[(-1)bso_47] ≥ 0)
    • (i69[6] ≥ 0∧i79[6] + i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)Bound*bni_46] + [(-1)bni_46]i69[6] ≥ 0∧[(-1)bso_47] ≥ 0)

  • COND_LOAD12223(TRUE, i79[13], i85[13], i69[13]) → LOAD1222(+(i79[13], -1), i85[13], i69[13])
    • (i69[12] ≥ 0∧i79[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧0 = 0∧[(-1)Bound*bni_48] + [bni_48]i79[12] ≥ 0∧0 = 0∧[(-1)bso_49] ≥ 0)
    • (i69[12] ≥ 0∧i79[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧0 = 0∧[(-1)Bound*bni_48] + [bni_48]i79[12] ≥ 0∧0 = 0∧[(-1)bso_49] ≥ 0)

  • LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])
    • (i69[12] ≥ 0∧i79[12] ≥ 0 ⇒ (UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥)∧0 = 0∧[(-1)Bound*bni_50 + bni_50] + [bni_50]i79[12] ≥ 0∧0 = 0∧[1 + (-1)bso_51] ≥ 0)

  • COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3])
    • ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_53] ≥ 0)
    • ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_53] ≥ 0)

  • LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])
    • (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)Bound*bni_54] + [(-1)bni_54]i79[2] ≥ 0∧[(-1)bso_55] ≥ 0)
    • (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)Bound*bni_54] + [(-1)bni_54]i79[2] ≥ 0∧[(-1)bso_55] ≥ 0)

  • COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1])
    • ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_57] ≥ 0)
    • ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_57] ≥ 0)
    • ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_57] ≥ 0)

  • LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])
    • (i69[0] + i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_58] + [(-1)bni_58]i69[0] + [(-1)bni_58]i79[0] ≥ 0∧[(-1)bso_59] ≥ 0)
    • (i69[0] ≥ 0∧i79[0] + i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_58] + [(-1)bni_58]i69[0] ≥ 0∧[(-1)bso_59] ≥ 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) = [3]   
POL(COND_LOAD12322(x1, x2, x3, x4)) = [-1] + [-1]x4 + x2   
POL(LOAD1222(x1, x2, x3)) = [-1]x3 + x1   
POL(+(x1, x2)) = x1 + x2   
POL(-1) = [-1]   
POL(LOAD1232(x1, x2, x3)) = [-1]x3 + x1   
POL(&&(x1, x2)) = [-1]   
POL(>=(x1, x2)) = [-1]   
POL(0) = 0   
POL(>(x1, x2)) = [-1]   
POL(COND_LOAD12321(x1, x2, x3, x4)) = [-1]x4 + x2   
POL(<=(x1, x2)) = [-1]   
POL(COND_LOAD12223(x1, x2, x3, x4)) = [-1] + [-1]x4 + x2   
POL(COND_LOAD1232(x1, x2, x3, x4)) = [-1]x4 + x2   
POL(COND_LOAD1222(x1, x2, x3, x4)) = [-1]x4 + x2   

The following pairs are in P>:

LOAD1232(i79[10], i85[10], i69[10]) → COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])
LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])

The following pairs are in Pbound:

COND_LOAD12322(TRUE, i79[11], i85[11], i69[11]) → LOAD1222(+(i79[11], -1), i85[11], i69[11])
LOAD1232(i79[10], i85[10], i69[10]) → COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])
COND_LOAD12223(TRUE, i79[13], i85[13], i69[13]) → LOAD1222(+(i79[13], -1), i85[13], i69[13])
LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])

The following pairs are in P≥:

COND_LOAD12322(TRUE, i79[11], i85[11], i69[11]) → LOAD1222(+(i79[11], -1), i85[11], i69[11])
COND_LOAD12321(TRUE, i79[7], i85[7], i69[7]) → LOAD1222(i79[7], +(i85[7], -1), i69[7])
LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])
COND_LOAD12223(TRUE, i79[13], i85[13], i69[13]) → LOAD1222(+(i79[13], -1), i85[13], i69[13])
COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3])
LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])
COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1])
LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])

There are no usable rules.

(54) Complex Obligation (AND)

(55) 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:
(11): COND_LOAD12322(TRUE, i79[11], i85[11], i69[11]) → LOAD1222(i79[11] + -1, i85[11], i69[11])
(7): COND_LOAD12321(TRUE, i79[7], i85[7], i69[7]) → LOAD1222(i79[7], i85[7] + -1, i69[7])
(6): LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(i69[6] >= 0 && i85[6] > i69[6] && i79[6] <= i69[6], i79[6], i85[6], i69[6])
(13): COND_LOAD12223(TRUE, i79[13], i85[13], i69[13]) → LOAD1222(i79[13] + -1, i85[13], i69[13])
(3): COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3])
(2): LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(i85[2] <= i69[2] && i79[2] <= i69[2], i79[2], i85[2], i69[2])
(1): COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1])
(0): LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(i69[0] >= 0 && i85[0] > i69[0] && i79[0] <= i69[0], i79[0], i85[0], i69[0])

(3) -> (0), if ((i79[3] →* i79[0])∧(i69[3] →* i69[0])∧(i85[3] →* i85[0]))


(7) -> (0), if ((i85[7] + -1 →* i85[0])∧(i79[7] →* i79[0])∧(i69[7] →* i69[0]))


(11) -> (0), if ((i79[11] + -1 →* i79[0])∧(i85[11] →* i85[0])∧(i69[11] →* i69[0]))


(13) -> (0), if ((i69[13] →* i69[0])∧(i79[13] + -1 →* i79[0])∧(i85[13] →* i85[0]))


(0) -> (1), if ((i79[0] →* i79[1])∧(i85[0] →* i85[1])∧(i69[0] →* i69[1])∧(i69[0] >= 0 && i85[0] > i69[0] && i79[0] <= i69[0] →* TRUE))


(1) -> (2), if ((i79[1] →* i79[2])∧(i69[1] →* i69[2])∧(i85[1] →* i85[2]))


(2) -> (3), if ((i85[2] →* i85[3])∧(i69[2] →* i69[3])∧(i85[2] <= i69[2] && i79[2] <= i69[2] →* TRUE)∧(i79[2] →* i79[3]))


(1) -> (6), if ((i79[1] →* i79[6])∧(i85[1] →* i85[6])∧(i69[1] →* i69[6]))


(6) -> (7), if ((i85[6] →* i85[7])∧(i69[6] >= 0 && i85[6] > i69[6] && i79[6] <= i69[6] →* TRUE)∧(i69[6] →* i69[7])∧(i79[6] →* i79[7]))



The set Q consists of the following terms:
Load1222(x0, x1, x2)
Cond_Load1222(TRUE, x0, x1, x2)
Load1232(x0, x1, x2)
Cond_Load1232(TRUE, x0, x1, x2)
Cond_Load12221(TRUE, x0, x1, x2)
Cond_Load12321(TRUE, x0, x1, x2)
Cond_Load12222(TRUE, x0, x1, x2)
Cond_Load12322(TRUE, x0, x1, x2)
Cond_Load12223(TRUE, x0, x1, x2)

(56) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes.

(57) 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:
(7): COND_LOAD12321(TRUE, i79[7], i85[7], i69[7]) → LOAD1222(i79[7], i85[7] + -1, i69[7])
(6): LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(i69[6] >= 0 && i85[6] > i69[6] && i79[6] <= i69[6], i79[6], i85[6], i69[6])
(3): COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3])
(2): LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(i85[2] <= i69[2] && i79[2] <= i69[2], i79[2], i85[2], i69[2])
(1): COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1])
(0): LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(i69[0] >= 0 && i85[0] > i69[0] && i79[0] <= i69[0], i79[0], i85[0], i69[0])

(3) -> (0), if ((i79[3] →* i79[0])∧(i69[3] →* i69[0])∧(i85[3] →* i85[0]))


(7) -> (0), if ((i85[7] + -1 →* i85[0])∧(i79[7] →* i79[0])∧(i69[7] →* i69[0]))


(0) -> (1), if ((i79[0] →* i79[1])∧(i85[0] →* i85[1])∧(i69[0] →* i69[1])∧(i69[0] >= 0 && i85[0] > i69[0] && i79[0] <= i69[0] →* TRUE))


(1) -> (2), if ((i79[1] →* i79[2])∧(i69[1] →* i69[2])∧(i85[1] →* i85[2]))


(2) -> (3), if ((i85[2] →* i85[3])∧(i69[2] →* i69[3])∧(i85[2] <= i69[2] && i79[2] <= i69[2] →* TRUE)∧(i79[2] →* i79[3]))


(1) -> (6), if ((i79[1] →* i79[6])∧(i85[1] →* i85[6])∧(i69[1] →* i69[6]))


(6) -> (7), if ((i85[6] →* i85[7])∧(i69[6] >= 0 && i85[6] > i69[6] && i79[6] <= i69[6] →* TRUE)∧(i69[6] →* i69[7])∧(i79[6] →* i79[7]))



The set Q consists of the following terms:
Load1222(x0, x1, x2)
Cond_Load1222(TRUE, x0, x1, x2)
Load1232(x0, x1, x2)
Cond_Load1232(TRUE, x0, x1, x2)
Cond_Load12221(TRUE, x0, x1, x2)
Cond_Load12321(TRUE, x0, x1, x2)
Cond_Load12222(TRUE, x0, x1, x2)
Cond_Load12322(TRUE, x0, x1, x2)
Cond_Load12223(TRUE, x0, x1, x2)

(58) IDPNonInfProof (SOUND transformation)

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


For Pair COND_LOAD12321(TRUE, i79[7], i85[7], i69[7]) → LOAD1222(i79[7], +(i85[7], -1), i69[7]) the following chains were created:
  • We consider the chain LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6]), COND_LOAD12321(TRUE, i79[7], i85[7], i69[7]) → LOAD1222(i79[7], +(i85[7], -1), i69[7]), LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]) which results in the following constraint:

    (1)    (i85[6]=i85[7]∧&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6]))=TRUE∧i69[6]=i69[7]∧i79[6]=i79[7]∧+(i85[7], -1)=i85[0]∧i79[7]=i79[0]∧i69[7]=i69[0] ⇒ COND_LOAD12321(TRUE, i79[7], i85[7], i69[7])≥NonInfC∧COND_LOAD12321(TRUE, i79[7], i85[7], i69[7])≥LOAD1222(i79[7], +(i85[7], -1), i69[7])∧(UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥))



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

    (2)    (<=(i79[6], i69[6])=TRUE∧>=(i69[6], 0)=TRUE∧>(i85[6], i69[6])=TRUE ⇒ COND_LOAD12321(TRUE, i79[6], i85[6], i69[6])≥NonInfC∧COND_LOAD12321(TRUE, i79[6], i85[6], i69[6])≥LOAD1222(i79[6], +(i85[6], -1), i69[6])∧(UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥))



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

    (3)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] + [-1] + [-1]i69[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)bni_30 + (-1)Bound*bni_30] + [bni_30]i85[6] ≥ 0∧[1 + (-1)bso_31] ≥ 0)



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

    (4)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] + [-1] + [-1]i69[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)bni_30 + (-1)Bound*bni_30] + [bni_30]i85[6] ≥ 0∧[1 + (-1)bso_31] ≥ 0)



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

    (5)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] + [-1] + [-1]i69[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)bni_30 + (-1)Bound*bni_30] + [bni_30]i85[6] ≥ 0∧[1 + (-1)bso_31] ≥ 0)



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

    (6)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_30] + [bni_30]i69[6] + [bni_30]i85[6] ≥ 0∧[1 + (-1)bso_31] ≥ 0)



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

    (7)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_30] + [bni_30]i69[6] + [bni_30]i85[6] ≥ 0∧[1 + (-1)bso_31] ≥ 0)


    (8)    (i69[6] + i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_30] + [bni_30]i69[6] + [bni_30]i85[6] ≥ 0∧[1 + (-1)bso_31] ≥ 0)



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

    (9)    (i69[6] ≥ 0∧i79[6] + i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_30] + [bni_30]i79[6] + [bni_30]i69[6] + [bni_30]i85[6] ≥ 0∧[1 + (-1)bso_31] ≥ 0)







For Pair LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6]) the following chains were created:
  • We consider the chain LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6]), COND_LOAD12321(TRUE, i79[7], i85[7], i69[7]) → LOAD1222(i79[7], +(i85[7], -1), i69[7]) which results in the following constraint:

    (10)    (i85[6]=i85[7]∧&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6]))=TRUE∧i69[6]=i69[7]∧i79[6]=i79[7] ⇒ LOAD1232(i79[6], i85[6], i69[6])≥NonInfC∧LOAD1232(i79[6], i85[6], i69[6])≥COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])∧(UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥))



    We simplified constraint (10) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (11)    (<=(i79[6], i69[6])=TRUE∧>=(i69[6], 0)=TRUE∧>(i85[6], i69[6])=TRUE ⇒ LOAD1232(i79[6], i85[6], i69[6])≥NonInfC∧LOAD1232(i79[6], i85[6], i69[6])≥COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])∧(UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥))



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

    (12)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] + [-1] + [-1]i69[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)bni_32 + (-1)Bound*bni_32] + [bni_32]i85[6] ≥ 0∧[(-1)bso_33] ≥ 0)



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

    (13)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] + [-1] + [-1]i69[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)bni_32 + (-1)Bound*bni_32] + [bni_32]i85[6] ≥ 0∧[(-1)bso_33] ≥ 0)



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

    (14)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] + [-1] + [-1]i69[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)bni_32 + (-1)Bound*bni_32] + [bni_32]i85[6] ≥ 0∧[(-1)bso_33] ≥ 0)



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

    (15)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)Bound*bni_32] + [bni_32]i69[6] + [bni_32]i85[6] ≥ 0∧[(-1)bso_33] ≥ 0)



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

    (16)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)Bound*bni_32] + [bni_32]i69[6] + [bni_32]i85[6] ≥ 0∧[(-1)bso_33] ≥ 0)


    (17)    (i69[6] + i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)Bound*bni_32] + [bni_32]i69[6] + [bni_32]i85[6] ≥ 0∧[(-1)bso_33] ≥ 0)



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

    (18)    (i69[6] ≥ 0∧i79[6] + i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)Bound*bni_32] + [bni_32]i79[6] + [bni_32]i69[6] + [bni_32]i85[6] ≥ 0∧[(-1)bso_33] ≥ 0)







For Pair COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3]) the following chains were created:
  • We consider the chain COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3]), LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]) which results in the following constraint:

    (19)    (i79[3]=i79[0]∧i69[3]=i69[0]∧i85[3]=i85[0] ⇒ COND_LOAD1232(TRUE, i79[3], i85[3], i69[3])≥NonInfC∧COND_LOAD1232(TRUE, i79[3], i85[3], i69[3])≥LOAD1222(i79[3], i85[3], i69[3])∧(UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥))



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

    (20)    (COND_LOAD1232(TRUE, i79[3], i85[3], i69[3])≥NonInfC∧COND_LOAD1232(TRUE, i79[3], i85[3], i69[3])≥LOAD1222(i79[3], i85[3], i69[3])∧(UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥))



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

    (21)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bso_35] ≥ 0)



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

    (22)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bso_35] ≥ 0)



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

    (23)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bso_35] ≥ 0)



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

    (24)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_35] ≥ 0)







For Pair LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2]) the following chains were created:
  • We consider the chain LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2]), COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3]) which results in the following constraint:

    (25)    (i85[2]=i85[3]∧i69[2]=i69[3]∧&&(<=(i85[2], i69[2]), <=(i79[2], i69[2]))=TRUE∧i79[2]=i79[3] ⇒ LOAD1232(i79[2], i85[2], i69[2])≥NonInfC∧LOAD1232(i79[2], i85[2], i69[2])≥COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])∧(UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥))



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

    (26)    (<=(i85[2], i69[2])=TRUE∧<=(i79[2], i69[2])=TRUE ⇒ LOAD1232(i79[2], i85[2], i69[2])≥NonInfC∧LOAD1232(i79[2], i85[2], i69[2])≥COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])∧(UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥))



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

    (27)    (i69[2] + [-1]i85[2] ≥ 0∧i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_36 + (-1)Bound*bni_36] + [bni_36]i85[2] ≥ 0∧[(-1)bso_37] ≥ 0)



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

    (28)    (i69[2] + [-1]i85[2] ≥ 0∧i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_36 + (-1)Bound*bni_36] + [bni_36]i85[2] ≥ 0∧[(-1)bso_37] ≥ 0)



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

    (29)    (i69[2] + [-1]i85[2] ≥ 0∧i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_36 + (-1)Bound*bni_36] + [bni_36]i85[2] ≥ 0∧[(-1)bso_37] ≥ 0)



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

    (30)    (i69[2] ≥ 0∧i85[2] + i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_36 + (-1)Bound*bni_36] + [bni_36]i85[2] ≥ 0∧[(-1)bso_37] ≥ 0)



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

    (31)    (i69[2] ≥ 0∧i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_36 + (-1)Bound*bni_36] + [bni_36]i85[2] ≥ 0∧[(-1)bso_37] ≥ 0)



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

    (32)    (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_36 + (-1)Bound*bni_36] + [(-1)bni_36]i85[2] ≥ 0∧[(-1)bso_37] ≥ 0)


    (33)    (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_36 + (-1)Bound*bni_36] + [bni_36]i85[2] ≥ 0∧[(-1)bso_37] ≥ 0)







For Pair COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1]) the following chains were created:
  • We consider the chain COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1]), LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2]) which results in the following constraint:

    (34)    (i79[1]=i79[2]∧i69[1]=i69[2]∧i85[1]=i85[2] ⇒ COND_LOAD1222(TRUE, i79[1], i85[1], i69[1])≥NonInfC∧COND_LOAD1222(TRUE, i79[1], i85[1], i69[1])≥LOAD1232(i79[1], i85[1], i69[1])∧(UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥))



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

    (35)    (COND_LOAD1222(TRUE, i79[1], i85[1], i69[1])≥NonInfC∧COND_LOAD1222(TRUE, i79[1], i85[1], i69[1])≥LOAD1232(i79[1], i85[1], i69[1])∧(UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥))



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

    (36)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_39] ≥ 0)



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

    (37)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_39] ≥ 0)



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

    (38)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_39] ≥ 0)



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

    (39)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_39] ≥ 0)



  • We consider the chain COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1]), LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6]) which results in the following constraint:

    (40)    (i79[1]=i79[6]∧i85[1]=i85[6]∧i69[1]=i69[6] ⇒ COND_LOAD1222(TRUE, i79[1], i85[1], i69[1])≥NonInfC∧COND_LOAD1222(TRUE, i79[1], i85[1], i69[1])≥LOAD1232(i79[1], i85[1], i69[1])∧(UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥))



    We simplified constraint (40) using rule (IV) which results in the following new constraint:

    (41)    (COND_LOAD1222(TRUE, i79[1], i85[1], i69[1])≥NonInfC∧COND_LOAD1222(TRUE, i79[1], i85[1], i69[1])≥LOAD1232(i79[1], i85[1], i69[1])∧(UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥))



    We simplified constraint (41) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (42)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_39] ≥ 0)



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

    (43)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_39] ≥ 0)



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

    (44)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_39] ≥ 0)



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

    (45)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_39] ≥ 0)







For Pair LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]) the following chains were created:
  • We consider the chain LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]), COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1]) which results in the following constraint:

    (46)    (i79[0]=i79[1]∧i85[0]=i85[1]∧i69[0]=i69[1]∧&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0]))=TRUE ⇒ LOAD1222(i79[0], i85[0], i69[0])≥NonInfC∧LOAD1222(i79[0], i85[0], i69[0])≥COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])∧(UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥))



    We simplified constraint (46) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (47)    (<=(i79[0], i69[0])=TRUE∧>=(i69[0], 0)=TRUE∧>(i85[0], i69[0])=TRUE ⇒ LOAD1222(i79[0], i85[0], i69[0])≥NonInfC∧LOAD1222(i79[0], i85[0], i69[0])≥COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])∧(UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥))



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

    (48)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] + [-1] + [-1]i69[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)bni_40 + (-1)Bound*bni_40] + [bni_40]i85[0] ≥ 0∧[(-1)bso_41] ≥ 0)



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

    (49)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] + [-1] + [-1]i69[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)bni_40 + (-1)Bound*bni_40] + [bni_40]i85[0] ≥ 0∧[(-1)bso_41] ≥ 0)



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

    (50)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] + [-1] + [-1]i69[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)bni_40 + (-1)Bound*bni_40] + [bni_40]i85[0] ≥ 0∧[(-1)bso_41] ≥ 0)



    We simplified constraint (50) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (51)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_40] + [bni_40]i69[0] + [bni_40]i85[0] ≥ 0∧[(-1)bso_41] ≥ 0)



    We simplified constraint (51) using rule (IDP_SMT_SPLIT) which results in the following new constraints:

    (52)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_40] + [bni_40]i69[0] + [bni_40]i85[0] ≥ 0∧[(-1)bso_41] ≥ 0)


    (53)    (i69[0] + i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_40] + [bni_40]i69[0] + [bni_40]i85[0] ≥ 0∧[(-1)bso_41] ≥ 0)



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

    (54)    (i69[0] ≥ 0∧i79[0] + i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_40] + [bni_40]i79[0] + [bni_40]i69[0] + [bni_40]i85[0] ≥ 0∧[(-1)bso_41] ≥ 0)







To summarize, we get the following constraints P≥ for the following pairs.
  • COND_LOAD12321(TRUE, i79[7], i85[7], i69[7]) → LOAD1222(i79[7], +(i85[7], -1), i69[7])
    • (i69[6] + i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_30] + [bni_30]i69[6] + [bni_30]i85[6] ≥ 0∧[1 + (-1)bso_31] ≥ 0)
    • (i69[6] ≥ 0∧i79[6] + i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_30] + [bni_30]i79[6] + [bni_30]i69[6] + [bni_30]i85[6] ≥ 0∧[1 + (-1)bso_31] ≥ 0)

  • LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])
    • (i69[6] + i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)Bound*bni_32] + [bni_32]i69[6] + [bni_32]i85[6] ≥ 0∧[(-1)bso_33] ≥ 0)
    • (i69[6] ≥ 0∧i79[6] + i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)Bound*bni_32] + [bni_32]i79[6] + [bni_32]i69[6] + [bni_32]i85[6] ≥ 0∧[(-1)bso_33] ≥ 0)

  • COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3])
    • ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_35] ≥ 0)

  • LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])
    • (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_36 + (-1)Bound*bni_36] + [(-1)bni_36]i85[2] ≥ 0∧[(-1)bso_37] ≥ 0)
    • (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_36 + (-1)Bound*bni_36] + [bni_36]i85[2] ≥ 0∧[(-1)bso_37] ≥ 0)

  • COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1])
    • ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_39] ≥ 0)
    • ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_39] ≥ 0)

  • LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])
    • (i69[0] + i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_40] + [bni_40]i69[0] + [bni_40]i85[0] ≥ 0∧[(-1)bso_41] ≥ 0)
    • (i69[0] ≥ 0∧i79[0] + i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_40] + [bni_40]i79[0] + [bni_40]i69[0] + [bni_40]i85[0] ≥ 0∧[(-1)bso_41] ≥ 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) = [3]   
POL(COND_LOAD12321(x1, x2, x3, x4)) = [-1] + x3   
POL(LOAD1222(x1, x2, x3)) = [-1] + x2   
POL(+(x1, x2)) = x1 + x2   
POL(-1) = [-1]   
POL(LOAD1232(x1, x2, x3)) = [-1] + x2   
POL(&&(x1, x2)) = [-1]   
POL(>=(x1, x2)) = [-1]   
POL(0) = 0   
POL(>(x1, x2)) = [-1]   
POL(<=(x1, x2)) = [-1]   
POL(COND_LOAD1232(x1, x2, x3, x4)) = [-1] + x3   
POL(COND_LOAD1222(x1, x2, x3, x4)) = [-1] + x3   

The following pairs are in P>:

COND_LOAD12321(TRUE, i79[7], i85[7], i69[7]) → LOAD1222(i79[7], +(i85[7], -1), i69[7])

The following pairs are in Pbound:

COND_LOAD12321(TRUE, i79[7], i85[7], i69[7]) → LOAD1222(i79[7], +(i85[7], -1), i69[7])
LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])
LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])

The following pairs are in P≥:

LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])
COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3])
LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])
COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1])
LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])

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

(59) Complex Obligation (AND)

(60) 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:
(6): LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(i69[6] >= 0 && i85[6] > i69[6] && i79[6] <= i69[6], i79[6], i85[6], i69[6])
(3): COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3])
(2): LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(i85[2] <= i69[2] && i79[2] <= i69[2], i79[2], i85[2], i69[2])
(1): COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1])
(0): LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(i69[0] >= 0 && i85[0] > i69[0] && i79[0] <= i69[0], i79[0], i85[0], i69[0])

(3) -> (0), if ((i79[3] →* i79[0])∧(i69[3] →* i69[0])∧(i85[3] →* i85[0]))


(0) -> (1), if ((i79[0] →* i79[1])∧(i85[0] →* i85[1])∧(i69[0] →* i69[1])∧(i69[0] >= 0 && i85[0] > i69[0] && i79[0] <= i69[0] →* TRUE))


(1) -> (2), if ((i79[1] →* i79[2])∧(i69[1] →* i69[2])∧(i85[1] →* i85[2]))


(2) -> (3), if ((i85[2] →* i85[3])∧(i69[2] →* i69[3])∧(i85[2] <= i69[2] && i79[2] <= i69[2] →* TRUE)∧(i79[2] →* i79[3]))


(1) -> (6), if ((i79[1] →* i79[6])∧(i85[1] →* i85[6])∧(i69[1] →* i69[6]))



The set Q consists of the following terms:
Load1222(x0, x1, x2)
Cond_Load1222(TRUE, x0, x1, x2)
Load1232(x0, x1, x2)
Cond_Load1232(TRUE, x0, x1, x2)
Cond_Load12221(TRUE, x0, x1, x2)
Cond_Load12321(TRUE, x0, x1, x2)
Cond_Load12222(TRUE, x0, x1, x2)
Cond_Load12322(TRUE, x0, x1, x2)
Cond_Load12223(TRUE, x0, x1, x2)

(61) IDependencyGraphProof (EQUIVALENT transformation)

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

(62) Obligation:

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


The following domains are used:

Boolean, Integer


R is empty.

The integer pair graph contains the following rules and edges:
(2): LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(i85[2] <= i69[2] && i79[2] <= i69[2], i79[2], i85[2], i69[2])
(1): COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1])
(0): LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(i69[0] >= 0 && i85[0] > i69[0] && i79[0] <= i69[0], i79[0], i85[0], i69[0])
(3): COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3])

(3) -> (0), if ((i79[3] →* i79[0])∧(i69[3] →* i69[0])∧(i85[3] →* i85[0]))


(0) -> (1), if ((i79[0] →* i79[1])∧(i85[0] →* i85[1])∧(i69[0] →* i69[1])∧(i69[0] >= 0 && i85[0] > i69[0] && i79[0] <= i69[0] →* TRUE))


(1) -> (2), if ((i79[1] →* i79[2])∧(i69[1] →* i69[2])∧(i85[1] →* i85[2]))


(2) -> (3), if ((i85[2] →* i85[3])∧(i69[2] →* i69[3])∧(i85[2] <= i69[2] && i79[2] <= i69[2] →* TRUE)∧(i79[2] →* i79[3]))



The set Q consists of the following terms:
Load1222(x0, x1, x2)
Cond_Load1222(TRUE, x0, x1, x2)
Load1232(x0, x1, x2)
Cond_Load1232(TRUE, x0, x1, x2)
Cond_Load12221(TRUE, x0, x1, x2)
Cond_Load12321(TRUE, x0, x1, x2)
Cond_Load12222(TRUE, x0, x1, x2)
Cond_Load12322(TRUE, x0, x1, x2)
Cond_Load12223(TRUE, x0, x1, x2)

(63) 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 LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2]) the following chains were created:
  • We consider the chain COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1]), LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2]), COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3]) which results in the following constraint:

    (1)    (i79[1]=i79[2]∧i69[1]=i69[2]∧i85[1]=i85[2]∧i85[2]=i85[3]∧i69[2]=i69[3]∧&&(<=(i85[2], i69[2]), <=(i79[2], i69[2]))=TRUE∧i79[2]=i79[3] ⇒ LOAD1232(i79[2], i85[2], i69[2])≥NonInfC∧LOAD1232(i79[2], i85[2], i69[2])≥COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])∧(UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥))



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

    (2)    (<=(i85[2], i69[2])=TRUE∧<=(i79[2], i69[2])=TRUE ⇒ LOAD1232(i79[2], i85[2], i69[2])≥NonInfC∧LOAD1232(i79[2], i85[2], i69[2])≥COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])∧(UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥))



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

    (3)    (i69[2] + [-1]i85[2] ≥ 0∧i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_25 + (-1)Bound*bni_25] + [(2)bni_25]i69[2] + [(-1)bni_25]i85[2] + [(-1)bni_25]i79[2] ≥ 0∧[(-1)bso_26] + [3]i69[2] + [-3]i85[2] ≥ 0)



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

    (4)    (i69[2] + [-1]i85[2] ≥ 0∧i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_25 + (-1)Bound*bni_25] + [(2)bni_25]i69[2] + [(-1)bni_25]i85[2] + [(-1)bni_25]i79[2] ≥ 0∧[(-1)bso_26] + [3]i69[2] + [-3]i85[2] ≥ 0)



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

    (5)    (i69[2] + [-1]i85[2] ≥ 0∧i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_25 + (-1)Bound*bni_25] + [(2)bni_25]i69[2] + [(-1)bni_25]i85[2] + [(-1)bni_25]i79[2] ≥ 0∧[(-1)bso_26] + [3]i69[2] + [-3]i85[2] ≥ 0)



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

    (6)    (i69[2] ≥ 0∧i85[2] + i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_25 + (-1)Bound*bni_25] + [bni_25]i85[2] + [(2)bni_25]i69[2] + [(-1)bni_25]i79[2] ≥ 0∧[(-1)bso_26] + [3]i69[2] ≥ 0)



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

    (7)    (i69[2] ≥ 0∧i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_25 + (-1)Bound*bni_25] + [bni_25]i69[2] + [bni_25]i79[2] ≥ 0∧[(-1)bso_26] + [3]i69[2] ≥ 0)



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

    (8)    (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_25 + (-1)Bound*bni_25] + [bni_25]i69[2] + [bni_25]i79[2] ≥ 0∧[(-1)bso_26] + [3]i69[2] ≥ 0)


    (9)    (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_25 + (-1)Bound*bni_25] + [bni_25]i69[2] + [bni_25]i79[2] ≥ 0∧[(-1)bso_26] + [3]i69[2] ≥ 0)







For Pair COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1]) the following chains were created:
  • We consider the chain LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]), COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1]), LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2]) which results in the following constraint:

    (10)    (i79[0]=i79[1]∧i85[0]=i85[1]∧i69[0]=i69[1]∧&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0]))=TRUE∧i79[1]=i79[2]∧i69[1]=i69[2]∧i85[1]=i85[2] ⇒ COND_LOAD1222(TRUE, i79[1], i85[1], i69[1])≥NonInfC∧COND_LOAD1222(TRUE, i79[1], i85[1], i69[1])≥LOAD1232(i79[1], i85[1], i69[1])∧(UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥))



    We simplified constraint (10) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (11)    (<=(i79[0], i69[0])=TRUE∧>=(i69[0], 0)=TRUE∧>(i85[0], i69[0])=TRUE ⇒ COND_LOAD1222(TRUE, i79[0], i85[0], i69[0])≥NonInfC∧COND_LOAD1222(TRUE, i79[0], i85[0], i69[0])≥LOAD1232(i79[0], i85[0], i69[0])∧(UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥))



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

    (12)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] + [-1] + [-1]i69[0] ≥ 0 ⇒ (UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)Bound*bni_27] + [(2)bni_27]i69[0] + [(-1)bni_27]i85[0] + [(-1)bni_27]i79[0] ≥ 0∧[1 + (-1)bso_28] ≥ 0)



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

    (13)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] + [-1] + [-1]i69[0] ≥ 0 ⇒ (UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)Bound*bni_27] + [(2)bni_27]i69[0] + [(-1)bni_27]i85[0] + [(-1)bni_27]i79[0] ≥ 0∧[1 + (-1)bso_28] ≥ 0)



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

    (14)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] + [-1] + [-1]i69[0] ≥ 0 ⇒ (UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)Bound*bni_27] + [(2)bni_27]i69[0] + [(-1)bni_27]i85[0] + [(-1)bni_27]i79[0] ≥ 0∧[1 + (-1)bso_28] ≥ 0)



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

    (15)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0 ⇒ (UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)Bound*bni_27 + (-1)bni_27] + [bni_27]i69[0] + [(-1)bni_27]i85[0] + [(-1)bni_27]i79[0] ≥ 0∧[1 + (-1)bso_28] ≥ 0)



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

    (16)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)Bound*bni_27 + (-1)bni_27] + [bni_27]i69[0] + [(-1)bni_27]i85[0] + [(-1)bni_27]i79[0] ≥ 0∧[1 + (-1)bso_28] ≥ 0)


    (17)    (i69[0] + i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)Bound*bni_27 + (-1)bni_27] + [bni_27]i69[0] + [(-1)bni_27]i85[0] + [bni_27]i79[0] ≥ 0∧[1 + (-1)bso_28] ≥ 0)



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

    (18)    (i69[0] ≥ 0∧i79[0] + i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)Bound*bni_27 + (-1)bni_27] + [bni_27]i69[0] + [(-1)bni_27]i85[0] ≥ 0∧[1 + (-1)bso_28] ≥ 0)







For Pair LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]) the following chains were created:
  • We consider the chain COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3]), LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]), COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1]) which results in the following constraint:

    (19)    (i79[3]=i79[0]∧i69[3]=i69[0]∧i85[3]=i85[0]∧i79[0]=i79[1]∧i85[0]=i85[1]∧i69[0]=i69[1]∧&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0]))=TRUE ⇒ LOAD1222(i79[0], i85[0], i69[0])≥NonInfC∧LOAD1222(i79[0], i85[0], i69[0])≥COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])∧(UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥))



    We simplified constraint (19) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (20)    (<=(i79[0], i69[0])=TRUE∧>=(i69[0], 0)=TRUE∧>(i85[0], i69[0])=TRUE ⇒ LOAD1222(i79[0], i85[0], i69[0])≥NonInfC∧LOAD1222(i79[0], i85[0], i69[0])≥COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])∧(UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥))



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

    (21)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] + [-1] + [-1]i69[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)bni_29 + (-1)Bound*bni_29] + [(-1)bni_29]i69[0] + [(2)bni_29]i85[0] + [(-1)bni_29]i79[0] ≥ 0∧[-2 + (-1)bso_30] + [-3]i69[0] + [3]i85[0] ≥ 0)



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

    (22)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] + [-1] + [-1]i69[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)bni_29 + (-1)Bound*bni_29] + [(-1)bni_29]i69[0] + [(2)bni_29]i85[0] + [(-1)bni_29]i79[0] ≥ 0∧[-2 + (-1)bso_30] + [-3]i69[0] + [3]i85[0] ≥ 0)



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

    (23)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] + [-1] + [-1]i69[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)bni_29 + (-1)Bound*bni_29] + [(-1)bni_29]i69[0] + [(2)bni_29]i85[0] + [(-1)bni_29]i79[0] ≥ 0∧[-2 + (-1)bso_30] + [-3]i69[0] + [3]i85[0] ≥ 0)



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

    (24)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[bni_29 + (-1)Bound*bni_29] + [bni_29]i69[0] + [(2)bni_29]i85[0] + [(-1)bni_29]i79[0] ≥ 0∧[1 + (-1)bso_30] + [3]i85[0] ≥ 0)



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

    (25)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[bni_29 + (-1)Bound*bni_29] + [bni_29]i69[0] + [(2)bni_29]i85[0] + [(-1)bni_29]i79[0] ≥ 0∧[1 + (-1)bso_30] + [3]i85[0] ≥ 0)


    (26)    (i69[0] + i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[bni_29 + (-1)Bound*bni_29] + [bni_29]i69[0] + [(2)bni_29]i85[0] + [bni_29]i79[0] ≥ 0∧[1 + (-1)bso_30] + [3]i85[0] ≥ 0)



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

    (27)    (i69[0] ≥ 0∧i79[0] + i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[bni_29 + (-1)Bound*bni_29] + [bni_29]i69[0] + [(2)bni_29]i85[0] ≥ 0∧[1 + (-1)bso_30] + [3]i85[0] ≥ 0)







For Pair COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3]) the following chains were created:
  • We consider the chain LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2]), COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3]), LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]) which results in the following constraint:

    (28)    (i85[2]=i85[3]∧i69[2]=i69[3]∧&&(<=(i85[2], i69[2]), <=(i79[2], i69[2]))=TRUE∧i79[2]=i79[3]∧i79[3]=i79[0]∧i69[3]=i69[0]∧i85[3]=i85[0] ⇒ COND_LOAD1232(TRUE, i79[3], i85[3], i69[3])≥NonInfC∧COND_LOAD1232(TRUE, i79[3], i85[3], i69[3])≥LOAD1222(i79[3], i85[3], i69[3])∧(UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥))



    We simplified constraint (28) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (29)    (<=(i85[2], i69[2])=TRUE∧<=(i79[2], i69[2])=TRUE ⇒ COND_LOAD1232(TRUE, i79[2], i85[2], i69[2])≥NonInfC∧COND_LOAD1232(TRUE, i79[2], i85[2], i69[2])≥LOAD1222(i79[2], i85[2], i69[2])∧(UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥))



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

    (30)    (i69[2] + [-1]i85[2] ≥ 0∧i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bni_31 + (-1)Bound*bni_31] + [(-1)bni_31]i69[2] + [(2)bni_31]i85[2] + [(-1)bni_31]i79[2] ≥ 0∧[(-1)bso_32] ≥ 0)



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

    (31)    (i69[2] + [-1]i85[2] ≥ 0∧i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bni_31 + (-1)Bound*bni_31] + [(-1)bni_31]i69[2] + [(2)bni_31]i85[2] + [(-1)bni_31]i79[2] ≥ 0∧[(-1)bso_32] ≥ 0)



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

    (32)    (i69[2] + [-1]i85[2] ≥ 0∧i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bni_31 + (-1)Bound*bni_31] + [(-1)bni_31]i69[2] + [(2)bni_31]i85[2] + [(-1)bni_31]i79[2] ≥ 0∧[(-1)bso_32] ≥ 0)



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

    (33)    (i69[2] ≥ 0∧i85[2] + i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bni_31 + (-1)Bound*bni_31] + [bni_31]i85[2] + [(-1)bni_31]i69[2] + [(-1)bni_31]i79[2] ≥ 0∧[(-1)bso_32] ≥ 0)



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

    (34)    (i69[2] ≥ 0∧i79[2] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bni_31 + (-1)Bound*bni_31] + [(-2)bni_31]i69[2] + [bni_31]i79[2] ≥ 0∧[(-1)bso_32] ≥ 0)



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

    (35)    (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bni_31 + (-1)Bound*bni_31] + [(-2)bni_31]i69[2] + [bni_31]i79[2] ≥ 0∧[(-1)bso_32] ≥ 0)


    (36)    (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bni_31 + (-1)Bound*bni_31] + [(-2)bni_31]i69[2] + [bni_31]i79[2] ≥ 0∧[(-1)bso_32] ≥ 0)







To summarize, we get the following constraints P≥ for the following pairs.
  • LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])
    • (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_25 + (-1)Bound*bni_25] + [bni_25]i69[2] + [bni_25]i79[2] ≥ 0∧[(-1)bso_26] + [3]i69[2] ≥ 0)
    • (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_25 + (-1)Bound*bni_25] + [bni_25]i69[2] + [bni_25]i79[2] ≥ 0∧[(-1)bso_26] + [3]i69[2] ≥ 0)

  • COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1])
    • (i69[0] + i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)Bound*bni_27 + (-1)bni_27] + [bni_27]i69[0] + [(-1)bni_27]i85[0] + [bni_27]i79[0] ≥ 0∧[1 + (-1)bso_28] ≥ 0)
    • (i69[0] ≥ 0∧i79[0] + i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)Bound*bni_27 + (-1)bni_27] + [bni_27]i69[0] + [(-1)bni_27]i85[0] ≥ 0∧[1 + (-1)bso_28] ≥ 0)

  • LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])
    • (i69[0] + i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[bni_29 + (-1)Bound*bni_29] + [bni_29]i69[0] + [(2)bni_29]i85[0] + [bni_29]i79[0] ≥ 0∧[1 + (-1)bso_30] + [3]i85[0] ≥ 0)
    • (i69[0] ≥ 0∧i79[0] + i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[bni_29 + (-1)Bound*bni_29] + [bni_29]i69[0] + [(2)bni_29]i85[0] ≥ 0∧[1 + (-1)bso_30] + [3]i85[0] ≥ 0)

  • COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3])
    • (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bni_31 + (-1)Bound*bni_31] + [(-2)bni_31]i69[2] + [bni_31]i79[2] ≥ 0∧[(-1)bso_32] ≥ 0)
    • (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bni_31 + (-1)Bound*bni_31] + [(-2)bni_31]i69[2] + [bni_31]i79[2] ≥ 0∧[(-1)bso_32] ≥ 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) = [2]   
POL(LOAD1232(x1, x2, x3)) = [-1] + [2]x3 + [-1]x2 + [-1]x1   
POL(COND_LOAD1232(x1, x2, x3, x4)) = [-1] + [-1]x4 + [2]x3 + [-1]x2   
POL(&&(x1, x2)) = [-1]   
POL(<=(x1, x2)) = [-1]   
POL(COND_LOAD1222(x1, x2, x3, x4)) = [2]x4 + [-1]x3 + [-1]x2 + [-1]x1   
POL(LOAD1222(x1, x2, x3)) = [-1] + [-1]x3 + [2]x2 + [-1]x1   
POL(>=(x1, x2)) = [-1]   
POL(0) = 0   
POL(>(x1, x2)) = [-1]   

The following pairs are in P>:

COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1])
LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])

The following pairs are in Pbound:

LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])
LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])

The following pairs are in P≥:

LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])
COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3])

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

(64) Complex Obligation (AND)

(65) Obligation:

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


The following domains are used:

Boolean, Integer


R is empty.

The integer pair graph contains the following rules and edges:
(2): LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(i85[2] <= i69[2] && i79[2] <= i69[2], i79[2], i85[2], i69[2])
(3): COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3])

(2) -> (3), if ((i85[2] →* i85[3])∧(i69[2] →* i69[3])∧(i85[2] <= i69[2] && i79[2] <= i69[2] →* TRUE)∧(i79[2] →* i79[3]))



The set Q consists of the following terms:
Load1222(x0, x1, x2)
Cond_Load1222(TRUE, x0, x1, x2)
Load1232(x0, x1, x2)
Cond_Load1232(TRUE, x0, x1, x2)
Cond_Load12221(TRUE, x0, x1, x2)
Cond_Load12321(TRUE, x0, x1, x2)
Cond_Load12222(TRUE, x0, x1, x2)
Cond_Load12322(TRUE, x0, x1, x2)
Cond_Load12223(TRUE, x0, x1, x2)

(66) IDependencyGraphProof (EQUIVALENT transformation)

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

(67) TRUE

(68) Obligation:

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


The following domains are used:
none


R is empty.

The integer pair graph contains the following rules and edges:
(1): COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1])
(3): COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3])


The set Q consists of the following terms:
Load1222(x0, x1, x2)
Cond_Load1222(TRUE, x0, x1, x2)
Load1232(x0, x1, x2)
Cond_Load1232(TRUE, x0, x1, x2)
Cond_Load12221(TRUE, x0, x1, x2)
Cond_Load12321(TRUE, x0, x1, x2)
Cond_Load12222(TRUE, x0, x1, x2)
Cond_Load12322(TRUE, x0, x1, x2)
Cond_Load12223(TRUE, x0, x1, x2)

(69) IDependencyGraphProof (EQUIVALENT transformation)

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

(70) TRUE

(71) 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:
(3): COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3])
(2): LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(i85[2] <= i69[2] && i79[2] <= i69[2], i79[2], i85[2], i69[2])
(1): COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1])

(1) -> (2), if ((i79[1] →* i79[2])∧(i69[1] →* i69[2])∧(i85[1] →* i85[2]))


(2) -> (3), if ((i85[2] →* i85[3])∧(i69[2] →* i69[3])∧(i85[2] <= i69[2] && i79[2] <= i69[2] →* TRUE)∧(i79[2] →* i79[3]))



The set Q consists of the following terms:
Load1222(x0, x1, x2)
Cond_Load1222(TRUE, x0, x1, x2)
Load1232(x0, x1, x2)
Cond_Load1232(TRUE, x0, x1, x2)
Cond_Load12221(TRUE, x0, x1, x2)
Cond_Load12321(TRUE, x0, x1, x2)
Cond_Load12222(TRUE, x0, x1, x2)
Cond_Load12322(TRUE, x0, x1, x2)
Cond_Load12223(TRUE, x0, x1, x2)

(72) IDependencyGraphProof (EQUIVALENT transformation)

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

(73) TRUE

(74) 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:
(7): COND_LOAD12321(TRUE, i79[7], i85[7], i69[7]) → LOAD1222(i79[7], i85[7] + -1, i69[7])
(6): LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(i69[6] >= 0 && i85[6] > i69[6] && i79[6] <= i69[6], i79[6], i85[6], i69[6])
(3): COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3])
(2): LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(i85[2] <= i69[2] && i79[2] <= i69[2], i79[2], i85[2], i69[2])
(1): COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1])
(0): LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(i69[0] >= 0 && i85[0] > i69[0] && i79[0] <= i69[0], i79[0], i85[0], i69[0])

(3) -> (0), if ((i79[3] →* i79[0])∧(i69[3] →* i69[0])∧(i85[3] →* i85[0]))


(7) -> (0), if ((i85[7] + -1 →* i85[0])∧(i79[7] →* i79[0])∧(i69[7] →* i69[0]))


(0) -> (1), if ((i79[0] →* i79[1])∧(i85[0] →* i85[1])∧(i69[0] →* i69[1])∧(i69[0] >= 0 && i85[0] > i69[0] && i79[0] <= i69[0] →* TRUE))


(1) -> (2), if ((i79[1] →* i79[2])∧(i69[1] →* i69[2])∧(i85[1] →* i85[2]))


(2) -> (3), if ((i85[2] →* i85[3])∧(i69[2] →* i69[3])∧(i85[2] <= i69[2] && i79[2] <= i69[2] →* TRUE)∧(i79[2] →* i79[3]))


(1) -> (6), if ((i79[1] →* i79[6])∧(i85[1] →* i85[6])∧(i69[1] →* i69[6]))


(6) -> (7), if ((i85[6] →* i85[7])∧(i69[6] >= 0 && i85[6] > i69[6] && i79[6] <= i69[6] →* TRUE)∧(i69[6] →* i69[7])∧(i79[6] →* i79[7]))



The set Q consists of the following terms:
Load1222(x0, x1, x2)
Cond_Load1222(TRUE, x0, x1, x2)
Load1232(x0, x1, x2)
Cond_Load1232(TRUE, x0, x1, x2)
Cond_Load12221(TRUE, x0, x1, x2)
Cond_Load12321(TRUE, x0, x1, x2)
Cond_Load12222(TRUE, x0, x1, x2)
Cond_Load12322(TRUE, x0, x1, x2)
Cond_Load12223(TRUE, x0, x1, x2)

(75) IDPNonInfProof (SOUND transformation)

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


For Pair COND_LOAD12321(TRUE, i79[7], i85[7], i69[7]) → LOAD1222(i79[7], +(i85[7], -1), i69[7]) the following chains were created:
  • We consider the chain LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6]), COND_LOAD12321(TRUE, i79[7], i85[7], i69[7]) → LOAD1222(i79[7], +(i85[7], -1), i69[7]), LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]) which results in the following constraint:

    (1)    (i85[6]=i85[7]∧&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6]))=TRUE∧i69[6]=i69[7]∧i79[6]=i79[7]∧+(i85[7], -1)=i85[0]∧i79[7]=i79[0]∧i69[7]=i69[0] ⇒ COND_LOAD12321(TRUE, i79[7], i85[7], i69[7])≥NonInfC∧COND_LOAD12321(TRUE, i79[7], i85[7], i69[7])≥LOAD1222(i79[7], +(i85[7], -1), i69[7])∧(UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥))



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

    (2)    (<=(i79[6], i69[6])=TRUE∧>=(i69[6], 0)=TRUE∧>(i85[6], i69[6])=TRUE ⇒ COND_LOAD12321(TRUE, i79[6], i85[6], i69[6])≥NonInfC∧COND_LOAD12321(TRUE, i79[6], i85[6], i69[6])≥LOAD1222(i79[6], +(i85[6], -1), i69[6])∧(UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥))



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

    (3)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] + [-1] + [-1]i69[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)bni_30 + (-1)Bound*bni_30] + [bni_30]i69[6] + [bni_30]i85[6] + [(-1)bni_30]i79[6] ≥ 0∧[1 + (-1)bso_31] ≥ 0)



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

    (4)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] + [-1] + [-1]i69[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)bni_30 + (-1)Bound*bni_30] + [bni_30]i69[6] + [bni_30]i85[6] + [(-1)bni_30]i79[6] ≥ 0∧[1 + (-1)bso_31] ≥ 0)



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

    (5)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] + [-1] + [-1]i69[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)bni_30 + (-1)Bound*bni_30] + [bni_30]i69[6] + [bni_30]i85[6] + [(-1)bni_30]i79[6] ≥ 0∧[1 + (-1)bso_31] ≥ 0)



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

    (6)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_30] + [(2)bni_30]i69[6] + [bni_30]i85[6] + [(-1)bni_30]i79[6] ≥ 0∧[1 + (-1)bso_31] ≥ 0)



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

    (7)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_30] + [(2)bni_30]i69[6] + [bni_30]i85[6] + [(-1)bni_30]i79[6] ≥ 0∧[1 + (-1)bso_31] ≥ 0)


    (8)    (i69[6] + i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_30] + [(2)bni_30]i69[6] + [bni_30]i85[6] + [bni_30]i79[6] ≥ 0∧[1 + (-1)bso_31] ≥ 0)



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

    (9)    (i69[6] ≥ 0∧i79[6] + i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_30] + [bni_30]i79[6] + [(2)bni_30]i69[6] + [bni_30]i85[6] ≥ 0∧[1 + (-1)bso_31] ≥ 0)







For Pair LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6]) the following chains were created:
  • We consider the chain LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6]), COND_LOAD12321(TRUE, i79[7], i85[7], i69[7]) → LOAD1222(i79[7], +(i85[7], -1), i69[7]) which results in the following constraint:

    (10)    (i85[6]=i85[7]∧&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6]))=TRUE∧i69[6]=i69[7]∧i79[6]=i79[7] ⇒ LOAD1232(i79[6], i85[6], i69[6])≥NonInfC∧LOAD1232(i79[6], i85[6], i69[6])≥COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])∧(UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥))



    We simplified constraint (10) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (11)    (<=(i79[6], i69[6])=TRUE∧>=(i69[6], 0)=TRUE∧>(i85[6], i69[6])=TRUE ⇒ LOAD1232(i79[6], i85[6], i69[6])≥NonInfC∧LOAD1232(i79[6], i85[6], i69[6])≥COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])∧(UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥))



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

    (12)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] + [-1] + [-1]i69[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)bni_32 + (-1)Bound*bni_32] + [bni_32]i69[6] + [bni_32]i85[6] + [(-1)bni_32]i79[6] ≥ 0∧[(-1)bso_33] ≥ 0)



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

    (13)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] + [-1] + [-1]i69[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)bni_32 + (-1)Bound*bni_32] + [bni_32]i69[6] + [bni_32]i85[6] + [(-1)bni_32]i79[6] ≥ 0∧[(-1)bso_33] ≥ 0)



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

    (14)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] + [-1] + [-1]i69[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)bni_32 + (-1)Bound*bni_32] + [bni_32]i69[6] + [bni_32]i85[6] + [(-1)bni_32]i79[6] ≥ 0∧[(-1)bso_33] ≥ 0)



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

    (15)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)Bound*bni_32] + [(2)bni_32]i69[6] + [bni_32]i85[6] + [(-1)bni_32]i79[6] ≥ 0∧[(-1)bso_33] ≥ 0)



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

    (16)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)Bound*bni_32] + [(2)bni_32]i69[6] + [bni_32]i85[6] + [(-1)bni_32]i79[6] ≥ 0∧[(-1)bso_33] ≥ 0)


    (17)    (i69[6] + i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)Bound*bni_32] + [(2)bni_32]i69[6] + [bni_32]i85[6] + [bni_32]i79[6] ≥ 0∧[(-1)bso_33] ≥ 0)



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

    (18)    (i69[6] ≥ 0∧i79[6] + i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)Bound*bni_32] + [bni_32]i79[6] + [(2)bni_32]i69[6] + [bni_32]i85[6] ≥ 0∧[(-1)bso_33] ≥ 0)







For Pair COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3]) the following chains were created:
  • We consider the chain COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3]), LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]) which results in the following constraint:

    (19)    (i79[3]=i79[0]∧i69[3]=i69[0]∧i85[3]=i85[0] ⇒ COND_LOAD1232(TRUE, i79[3], i85[3], i69[3])≥NonInfC∧COND_LOAD1232(TRUE, i79[3], i85[3], i69[3])≥LOAD1222(i79[3], i85[3], i69[3])∧(UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥))



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

    (20)    (COND_LOAD1232(TRUE, i79[3], i85[3], i69[3])≥NonInfC∧COND_LOAD1232(TRUE, i79[3], i85[3], i69[3])≥LOAD1222(i79[3], i85[3], i69[3])∧(UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥))



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

    (21)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bso_35] ≥ 0)



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

    (22)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bso_35] ≥ 0)



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

    (23)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bso_35] ≥ 0)



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

    (24)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_35] ≥ 0)







For Pair LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2]) the following chains were created:
  • We consider the chain LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2]), COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3]) which results in the following constraint:

    (25)    (i85[2]=i85[3]∧i69[2]=i69[3]∧&&(<=(i85[2], i69[2]), <=(i79[2], i69[2]))=TRUE∧i79[2]=i79[3] ⇒ LOAD1232(i79[2], i85[2], i69[2])≥NonInfC∧LOAD1232(i79[2], i85[2], i69[2])≥COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])∧(UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥))



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

    (26)    (<=(i85[2], i69[2])=TRUE∧<=(i79[2], i69[2])=TRUE ⇒ LOAD1232(i79[2], i85[2], i69[2])≥NonInfC∧LOAD1232(i79[2], i85[2], i69[2])≥COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])∧(UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥))



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

    (27)    (i69[2] + [-1]i85[2] ≥ 0∧i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_36 + (-1)Bound*bni_36] + [bni_36]i69[2] + [bni_36]i85[2] + [(-1)bni_36]i79[2] ≥ 0∧[(-1)bso_37] ≥ 0)



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

    (28)    (i69[2] + [-1]i85[2] ≥ 0∧i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_36 + (-1)Bound*bni_36] + [bni_36]i69[2] + [bni_36]i85[2] + [(-1)bni_36]i79[2] ≥ 0∧[(-1)bso_37] ≥ 0)



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

    (29)    (i69[2] + [-1]i85[2] ≥ 0∧i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_36 + (-1)Bound*bni_36] + [bni_36]i69[2] + [bni_36]i85[2] + [(-1)bni_36]i79[2] ≥ 0∧[(-1)bso_37] ≥ 0)



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

    (30)    (i69[2] ≥ 0∧i85[2] + i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_36 + (-1)Bound*bni_36] + [(2)bni_36]i85[2] + [bni_36]i69[2] + [(-1)bni_36]i79[2] ≥ 0∧[(-1)bso_37] ≥ 0)



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

    (31)    (i69[2] ≥ 0∧i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_36 + (-1)Bound*bni_36] + [bni_36]i85[2] + [bni_36]i79[2] ≥ 0∧[(-1)bso_37] ≥ 0)



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

    (32)    (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_36 + (-1)Bound*bni_36] + [bni_36]i85[2] + [bni_36]i79[2] ≥ 0∧[(-1)bso_37] ≥ 0)


    (33)    (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_36 + (-1)Bound*bni_36] + [(-1)bni_36]i85[2] + [bni_36]i79[2] ≥ 0∧[(-1)bso_37] ≥ 0)







For Pair COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1]) the following chains were created:
  • We consider the chain COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1]), LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2]) which results in the following constraint:

    (34)    (i79[1]=i79[2]∧i69[1]=i69[2]∧i85[1]=i85[2] ⇒ COND_LOAD1222(TRUE, i79[1], i85[1], i69[1])≥NonInfC∧COND_LOAD1222(TRUE, i79[1], i85[1], i69[1])≥LOAD1232(i79[1], i85[1], i69[1])∧(UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥))



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

    (35)    (COND_LOAD1222(TRUE, i79[1], i85[1], i69[1])≥NonInfC∧COND_LOAD1222(TRUE, i79[1], i85[1], i69[1])≥LOAD1232(i79[1], i85[1], i69[1])∧(UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥))



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

    (36)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_39] ≥ 0)



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

    (37)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_39] ≥ 0)



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

    (38)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_39] ≥ 0)



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

    (39)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_39] ≥ 0)



  • We consider the chain COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1]), LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6]) which results in the following constraint:

    (40)    (i79[1]=i79[6]∧i85[1]=i85[6]∧i69[1]=i69[6] ⇒ COND_LOAD1222(TRUE, i79[1], i85[1], i69[1])≥NonInfC∧COND_LOAD1222(TRUE, i79[1], i85[1], i69[1])≥LOAD1232(i79[1], i85[1], i69[1])∧(UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥))



    We simplified constraint (40) using rule (IV) which results in the following new constraint:

    (41)    (COND_LOAD1222(TRUE, i79[1], i85[1], i69[1])≥NonInfC∧COND_LOAD1222(TRUE, i79[1], i85[1], i69[1])≥LOAD1232(i79[1], i85[1], i69[1])∧(UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥))



    We simplified constraint (41) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (42)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_39] ≥ 0)



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

    (43)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_39] ≥ 0)



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

    (44)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_39] ≥ 0)



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

    (45)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_39] ≥ 0)







For Pair LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]) the following chains were created:
  • We consider the chain LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]), COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1]) which results in the following constraint:

    (46)    (i79[0]=i79[1]∧i85[0]=i85[1]∧i69[0]=i69[1]∧&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0]))=TRUE ⇒ LOAD1222(i79[0], i85[0], i69[0])≥NonInfC∧LOAD1222(i79[0], i85[0], i69[0])≥COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])∧(UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥))



    We simplified constraint (46) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (47)    (<=(i79[0], i69[0])=TRUE∧>=(i69[0], 0)=TRUE∧>(i85[0], i69[0])=TRUE ⇒ LOAD1222(i79[0], i85[0], i69[0])≥NonInfC∧LOAD1222(i79[0], i85[0], i69[0])≥COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])∧(UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥))



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

    (48)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] + [-1] + [-1]i69[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)bni_40 + (-1)Bound*bni_40] + [bni_40]i69[0] + [bni_40]i85[0] + [(-1)bni_40]i79[0] ≥ 0∧[(-1)bso_41] ≥ 0)



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

    (49)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] + [-1] + [-1]i69[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)bni_40 + (-1)Bound*bni_40] + [bni_40]i69[0] + [bni_40]i85[0] + [(-1)bni_40]i79[0] ≥ 0∧[(-1)bso_41] ≥ 0)



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

    (50)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] + [-1] + [-1]i69[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)bni_40 + (-1)Bound*bni_40] + [bni_40]i69[0] + [bni_40]i85[0] + [(-1)bni_40]i79[0] ≥ 0∧[(-1)bso_41] ≥ 0)



    We simplified constraint (50) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (51)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_40] + [(2)bni_40]i69[0] + [bni_40]i85[0] + [(-1)bni_40]i79[0] ≥ 0∧[(-1)bso_41] ≥ 0)



    We simplified constraint (51) using rule (IDP_SMT_SPLIT) which results in the following new constraints:

    (52)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_40] + [(2)bni_40]i69[0] + [bni_40]i85[0] + [(-1)bni_40]i79[0] ≥ 0∧[(-1)bso_41] ≥ 0)


    (53)    (i69[0] + i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_40] + [(2)bni_40]i69[0] + [bni_40]i85[0] + [bni_40]i79[0] ≥ 0∧[(-1)bso_41] ≥ 0)



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

    (54)    (i69[0] ≥ 0∧i79[0] + i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_40] + [bni_40]i79[0] + [(2)bni_40]i69[0] + [bni_40]i85[0] ≥ 0∧[(-1)bso_41] ≥ 0)







To summarize, we get the following constraints P≥ for the following pairs.
  • COND_LOAD12321(TRUE, i79[7], i85[7], i69[7]) → LOAD1222(i79[7], +(i85[7], -1), i69[7])
    • (i69[6] + i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_30] + [(2)bni_30]i69[6] + [bni_30]i85[6] + [bni_30]i79[6] ≥ 0∧[1 + (-1)bso_31] ≥ 0)
    • (i69[6] ≥ 0∧i79[6] + i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_30] + [bni_30]i79[6] + [(2)bni_30]i69[6] + [bni_30]i85[6] ≥ 0∧[1 + (-1)bso_31] ≥ 0)

  • LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])
    • (i69[6] + i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)Bound*bni_32] + [(2)bni_32]i69[6] + [bni_32]i85[6] + [bni_32]i79[6] ≥ 0∧[(-1)bso_33] ≥ 0)
    • (i69[6] ≥ 0∧i79[6] + i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)Bound*bni_32] + [bni_32]i79[6] + [(2)bni_32]i69[6] + [bni_32]i85[6] ≥ 0∧[(-1)bso_33] ≥ 0)

  • COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3])
    • ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_35] ≥ 0)

  • LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])
    • (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_36 + (-1)Bound*bni_36] + [bni_36]i85[2] + [bni_36]i79[2] ≥ 0∧[(-1)bso_37] ≥ 0)
    • (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_36 + (-1)Bound*bni_36] + [(-1)bni_36]i85[2] + [bni_36]i79[2] ≥ 0∧[(-1)bso_37] ≥ 0)

  • COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1])
    • ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_39] ≥ 0)
    • ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_39] ≥ 0)

  • LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])
    • (i69[0] + i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_40] + [(2)bni_40]i69[0] + [bni_40]i85[0] + [bni_40]i79[0] ≥ 0∧[(-1)bso_41] ≥ 0)
    • (i69[0] ≥ 0∧i79[0] + i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_40] + [bni_40]i79[0] + [(2)bni_40]i69[0] + [bni_40]i85[0] ≥ 0∧[(-1)bso_41] ≥ 0)




The constraints for P> respective Pbound are constructed from P≥ where we just replace every occurence of "t ≥ s" in P≥ by "t > s" respective "t ≥ c". Here c stands for the fresh constant used for Pbound.
Using the following integer polynomial ordering the resulting constraints can be solved
Polynomial interpretation over integers[POLO]:

POL(TRUE) = 0   
POL(FALSE) = 0   
POL(COND_LOAD12321(x1, x2, x3, x4)) = [-1] + x4 + x3 + [-1]x2   
POL(LOAD1222(x1, x2, x3)) = [-1] + x3 + x2 + [-1]x1   
POL(+(x1, x2)) = x1 + x2   
POL(-1) = [-1]   
POL(LOAD1232(x1, x2, x3)) = [-1] + x3 + x2 + [-1]x1   
POL(&&(x1, x2)) = [-1]   
POL(>=(x1, x2)) = [-1]   
POL(0) = 0   
POL(>(x1, x2)) = [-1]   
POL(<=(x1, x2)) = [-1]   
POL(COND_LOAD1232(x1, x2, x3, x4)) = [-1] + x4 + x3 + [-1]x2   
POL(COND_LOAD1222(x1, x2, x3, x4)) = [-1] + x4 + x3 + [-1]x2   

The following pairs are in P>:

COND_LOAD12321(TRUE, i79[7], i85[7], i69[7]) → LOAD1222(i79[7], +(i85[7], -1), i69[7])

The following pairs are in Pbound:

COND_LOAD12321(TRUE, i79[7], i85[7], i69[7]) → LOAD1222(i79[7], +(i85[7], -1), i69[7])
LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])
LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])

The following pairs are in P≥:

LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])
COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3])
LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])
COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1])
LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])

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

(76) Complex Obligation (AND)

(77) 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:
(6): LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(i69[6] >= 0 && i85[6] > i69[6] && i79[6] <= i69[6], i79[6], i85[6], i69[6])
(3): COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3])
(2): LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(i85[2] <= i69[2] && i79[2] <= i69[2], i79[2], i85[2], i69[2])
(1): COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1])
(0): LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(i69[0] >= 0 && i85[0] > i69[0] && i79[0] <= i69[0], i79[0], i85[0], i69[0])

(3) -> (0), if ((i79[3] →* i79[0])∧(i69[3] →* i69[0])∧(i85[3] →* i85[0]))


(0) -> (1), if ((i79[0] →* i79[1])∧(i85[0] →* i85[1])∧(i69[0] →* i69[1])∧(i69[0] >= 0 && i85[0] > i69[0] && i79[0] <= i69[0] →* TRUE))


(1) -> (2), if ((i79[1] →* i79[2])∧(i69[1] →* i69[2])∧(i85[1] →* i85[2]))


(2) -> (3), if ((i85[2] →* i85[3])∧(i69[2] →* i69[3])∧(i85[2] <= i69[2] && i79[2] <= i69[2] →* TRUE)∧(i79[2] →* i79[3]))


(1) -> (6), if ((i79[1] →* i79[6])∧(i85[1] →* i85[6])∧(i69[1] →* i69[6]))



The set Q consists of the following terms:
Load1222(x0, x1, x2)
Cond_Load1222(TRUE, x0, x1, x2)
Load1232(x0, x1, x2)
Cond_Load1232(TRUE, x0, x1, x2)
Cond_Load12221(TRUE, x0, x1, x2)
Cond_Load12321(TRUE, x0, x1, x2)
Cond_Load12222(TRUE, x0, x1, x2)
Cond_Load12322(TRUE, x0, x1, x2)
Cond_Load12223(TRUE, x0, x1, x2)

(78) IDependencyGraphProof (EQUIVALENT transformation)

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

(79) Obligation:

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


The following domains are used:

Boolean, Integer


R is empty.

The integer pair graph contains the following rules and edges:
(2): LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(i85[2] <= i69[2] && i79[2] <= i69[2], i79[2], i85[2], i69[2])
(1): COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1])
(0): LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(i69[0] >= 0 && i85[0] > i69[0] && i79[0] <= i69[0], i79[0], i85[0], i69[0])
(3): COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3])

(3) -> (0), if ((i79[3] →* i79[0])∧(i69[3] →* i69[0])∧(i85[3] →* i85[0]))


(0) -> (1), if ((i79[0] →* i79[1])∧(i85[0] →* i85[1])∧(i69[0] →* i69[1])∧(i69[0] >= 0 && i85[0] > i69[0] && i79[0] <= i69[0] →* TRUE))


(1) -> (2), if ((i79[1] →* i79[2])∧(i69[1] →* i69[2])∧(i85[1] →* i85[2]))


(2) -> (3), if ((i85[2] →* i85[3])∧(i69[2] →* i69[3])∧(i85[2] <= i69[2] && i79[2] <= i69[2] →* TRUE)∧(i79[2] →* i79[3]))



The set Q consists of the following terms:
Load1222(x0, x1, x2)
Cond_Load1222(TRUE, x0, x1, x2)
Load1232(x0, x1, x2)
Cond_Load1232(TRUE, x0, x1, x2)
Cond_Load12221(TRUE, x0, x1, x2)
Cond_Load12321(TRUE, x0, x1, x2)
Cond_Load12222(TRUE, x0, x1, x2)
Cond_Load12322(TRUE, x0, x1, x2)
Cond_Load12223(TRUE, x0, x1, x2)

(80) 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 LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2]) the following chains were created:
  • We consider the chain COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1]), LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2]), COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3]) which results in the following constraint:

    (1)    (i79[1]=i79[2]∧i69[1]=i69[2]∧i85[1]=i85[2]∧i85[2]=i85[3]∧i69[2]=i69[3]∧&&(<=(i85[2], i69[2]), <=(i79[2], i69[2]))=TRUE∧i79[2]=i79[3] ⇒ LOAD1232(i79[2], i85[2], i69[2])≥NonInfC∧LOAD1232(i79[2], i85[2], i69[2])≥COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])∧(UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥))



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

    (2)    (<=(i85[2], i69[2])=TRUE∧<=(i79[2], i69[2])=TRUE ⇒ LOAD1232(i79[2], i85[2], i69[2])≥NonInfC∧LOAD1232(i79[2], i85[2], i69[2])≥COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])∧(UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥))



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

    (3)    (i69[2] + [-1]i85[2] ≥ 0∧i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)Bound*bni_25] + [bni_25]i69[2] + [(-1)bni_25]i79[2] ≥ 0∧[(-1)bso_26] ≥ 0)



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

    (4)    (i69[2] + [-1]i85[2] ≥ 0∧i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)Bound*bni_25] + [bni_25]i69[2] + [(-1)bni_25]i79[2] ≥ 0∧[(-1)bso_26] ≥ 0)



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

    (5)    (i69[2] + [-1]i85[2] ≥ 0∧i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)Bound*bni_25] + [bni_25]i69[2] + [(-1)bni_25]i79[2] ≥ 0∧[(-1)bso_26] ≥ 0)



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

    (6)    (i69[2] ≥ 0∧i85[2] + i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)Bound*bni_25] + [bni_25]i85[2] + [bni_25]i69[2] + [(-1)bni_25]i79[2] ≥ 0∧[(-1)bso_26] ≥ 0)



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

    (7)    (i69[2] ≥ 0∧i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)Bound*bni_25] + [bni_25]i79[2] ≥ 0∧[(-1)bso_26] ≥ 0)



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

    (8)    (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)Bound*bni_25] + [bni_25]i79[2] ≥ 0∧[(-1)bso_26] ≥ 0)


    (9)    (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)Bound*bni_25] + [bni_25]i79[2] ≥ 0∧[(-1)bso_26] ≥ 0)







For Pair COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1]) the following chains were created:
  • We consider the chain LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]), COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1]), LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2]) which results in the following constraint:

    (10)    (i79[0]=i79[1]∧i85[0]=i85[1]∧i69[0]=i69[1]∧&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0]))=TRUE∧i79[1]=i79[2]∧i69[1]=i69[2]∧i85[1]=i85[2] ⇒ COND_LOAD1222(TRUE, i79[1], i85[1], i69[1])≥NonInfC∧COND_LOAD1222(TRUE, i79[1], i85[1], i69[1])≥LOAD1232(i79[1], i85[1], i69[1])∧(UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥))



    We simplified constraint (10) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (11)    (<=(i79[0], i69[0])=TRUE∧>=(i69[0], 0)=TRUE∧>(i85[0], i69[0])=TRUE ⇒ COND_LOAD1222(TRUE, i79[0], i85[0], i69[0])≥NonInfC∧COND_LOAD1222(TRUE, i79[0], i85[0], i69[0])≥LOAD1232(i79[0], i85[0], i69[0])∧(UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥))



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

    (12)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] + [-1] + [-1]i69[0] ≥ 0 ⇒ (UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bni_27 + (-1)Bound*bni_27] + [bni_27]i85[0] + [(-1)bni_27]i79[0] ≥ 0∧[-1 + (-1)bso_28] + [-1]i69[0] + i85[0] ≥ 0)



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

    (13)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] + [-1] + [-1]i69[0] ≥ 0 ⇒ (UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bni_27 + (-1)Bound*bni_27] + [bni_27]i85[0] + [(-1)bni_27]i79[0] ≥ 0∧[-1 + (-1)bso_28] + [-1]i69[0] + i85[0] ≥ 0)



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

    (14)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] + [-1] + [-1]i69[0] ≥ 0 ⇒ (UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bni_27 + (-1)Bound*bni_27] + [bni_27]i85[0] + [(-1)bni_27]i79[0] ≥ 0∧[-1 + (-1)bso_28] + [-1]i69[0] + i85[0] ≥ 0)



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

    (15)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0 ⇒ (UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)Bound*bni_27] + [bni_27]i69[0] + [bni_27]i85[0] + [(-1)bni_27]i79[0] ≥ 0∧[(-1)bso_28] + i85[0] ≥ 0)



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

    (16)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)Bound*bni_27] + [bni_27]i69[0] + [bni_27]i85[0] + [(-1)bni_27]i79[0] ≥ 0∧[(-1)bso_28] + i85[0] ≥ 0)


    (17)    (i69[0] + i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)Bound*bni_27] + [bni_27]i69[0] + [bni_27]i85[0] + [bni_27]i79[0] ≥ 0∧[(-1)bso_28] + i85[0] ≥ 0)



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

    (18)    (i69[0] ≥ 0∧i79[0] + i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)Bound*bni_27] + [bni_27]i69[0] + [bni_27]i85[0] ≥ 0∧[(-1)bso_28] + i85[0] ≥ 0)







For Pair LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]) the following chains were created:
  • We consider the chain COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3]), LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]), COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1]) which results in the following constraint:

    (19)    (i79[3]=i79[0]∧i69[3]=i69[0]∧i85[3]=i85[0]∧i79[0]=i79[1]∧i85[0]=i85[1]∧i69[0]=i69[1]∧&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0]))=TRUE ⇒ LOAD1222(i79[0], i85[0], i69[0])≥NonInfC∧LOAD1222(i79[0], i85[0], i69[0])≥COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])∧(UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥))



    We simplified constraint (19) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (20)    (<=(i79[0], i69[0])=TRUE∧>=(i69[0], 0)=TRUE∧>(i85[0], i69[0])=TRUE ⇒ LOAD1222(i79[0], i85[0], i69[0])≥NonInfC∧LOAD1222(i79[0], i85[0], i69[0])≥COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])∧(UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥))



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

    (21)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] + [-1] + [-1]i69[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)bni_29 + (-1)Bound*bni_29] + [bni_29]i85[0] + [(-1)bni_29]i79[0] ≥ 0∧[(-1)bso_30] ≥ 0)



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

    (22)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] + [-1] + [-1]i69[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)bni_29 + (-1)Bound*bni_29] + [bni_29]i85[0] + [(-1)bni_29]i79[0] ≥ 0∧[(-1)bso_30] ≥ 0)



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

    (23)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] + [-1] + [-1]i69[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)bni_29 + (-1)Bound*bni_29] + [bni_29]i85[0] + [(-1)bni_29]i79[0] ≥ 0∧[(-1)bso_30] ≥ 0)



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

    (24)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_29] + [bni_29]i69[0] + [bni_29]i85[0] + [(-1)bni_29]i79[0] ≥ 0∧[(-1)bso_30] ≥ 0)



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

    (25)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_29] + [bni_29]i69[0] + [bni_29]i85[0] + [(-1)bni_29]i79[0] ≥ 0∧[(-1)bso_30] ≥ 0)


    (26)    (i69[0] + i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_29] + [bni_29]i69[0] + [bni_29]i85[0] + [bni_29]i79[0] ≥ 0∧[(-1)bso_30] ≥ 0)



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

    (27)    (i69[0] ≥ 0∧i79[0] + i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_29] + [bni_29]i69[0] + [bni_29]i85[0] ≥ 0∧[(-1)bso_30] ≥ 0)







For Pair COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3]) the following chains were created:
  • We consider the chain LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2]), COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3]), LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]) which results in the following constraint:

    (28)    (i85[2]=i85[3]∧i69[2]=i69[3]∧&&(<=(i85[2], i69[2]), <=(i79[2], i69[2]))=TRUE∧i79[2]=i79[3]∧i79[3]=i79[0]∧i69[3]=i69[0]∧i85[3]=i85[0] ⇒ COND_LOAD1232(TRUE, i79[3], i85[3], i69[3])≥NonInfC∧COND_LOAD1232(TRUE, i79[3], i85[3], i69[3])≥LOAD1222(i79[3], i85[3], i69[3])∧(UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥))



    We simplified constraint (28) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (29)    (<=(i85[2], i69[2])=TRUE∧<=(i79[2], i69[2])=TRUE ⇒ COND_LOAD1232(TRUE, i79[2], i85[2], i69[2])≥NonInfC∧COND_LOAD1232(TRUE, i79[2], i85[2], i69[2])≥LOAD1222(i79[2], i85[2], i69[2])∧(UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥))



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

    (30)    (i69[2] + [-1]i85[2] ≥ 0∧i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)Bound*bni_31] + [bni_31]i69[2] + [(-1)bni_31]i79[2] ≥ 0∧[1 + (-1)bso_32] + i69[2] + [-1]i85[2] ≥ 0)



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

    (31)    (i69[2] + [-1]i85[2] ≥ 0∧i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)Bound*bni_31] + [bni_31]i69[2] + [(-1)bni_31]i79[2] ≥ 0∧[1 + (-1)bso_32] + i69[2] + [-1]i85[2] ≥ 0)



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

    (32)    (i69[2] + [-1]i85[2] ≥ 0∧i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)Bound*bni_31] + [bni_31]i69[2] + [(-1)bni_31]i79[2] ≥ 0∧[1 + (-1)bso_32] + i69[2] + [-1]i85[2] ≥ 0)



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

    (33)    (i69[2] ≥ 0∧i85[2] + i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)Bound*bni_31] + [bni_31]i85[2] + [bni_31]i69[2] + [(-1)bni_31]i79[2] ≥ 0∧[1 + (-1)bso_32] + i69[2] ≥ 0)



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

    (34)    (i69[2] ≥ 0∧i79[2] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)Bound*bni_31] + [bni_31]i79[2] ≥ 0∧[1 + (-1)bso_32] + i69[2] ≥ 0)



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

    (35)    (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)Bound*bni_31] + [bni_31]i79[2] ≥ 0∧[1 + (-1)bso_32] + i69[2] ≥ 0)


    (36)    (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)Bound*bni_31] + [bni_31]i79[2] ≥ 0∧[1 + (-1)bso_32] + i69[2] ≥ 0)







To summarize, we get the following constraints P≥ for the following pairs.
  • LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])
    • (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)Bound*bni_25] + [bni_25]i79[2] ≥ 0∧[(-1)bso_26] ≥ 0)
    • (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)Bound*bni_25] + [bni_25]i79[2] ≥ 0∧[(-1)bso_26] ≥ 0)

  • COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1])
    • (i69[0] + i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)Bound*bni_27] + [bni_27]i69[0] + [bni_27]i85[0] + [bni_27]i79[0] ≥ 0∧[(-1)bso_28] + i85[0] ≥ 0)
    • (i69[0] ≥ 0∧i79[0] + i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)Bound*bni_27] + [bni_27]i69[0] + [bni_27]i85[0] ≥ 0∧[(-1)bso_28] + i85[0] ≥ 0)

  • LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])
    • (i69[0] + i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_29] + [bni_29]i69[0] + [bni_29]i85[0] + [bni_29]i79[0] ≥ 0∧[(-1)bso_30] ≥ 0)
    • (i69[0] ≥ 0∧i79[0] + i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_29] + [bni_29]i69[0] + [bni_29]i85[0] ≥ 0∧[(-1)bso_30] ≥ 0)

  • COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3])
    • (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)Bound*bni_31] + [bni_31]i79[2] ≥ 0∧[1 + (-1)bso_32] + i69[2] ≥ 0)
    • (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)Bound*bni_31] + [bni_31]i79[2] ≥ 0∧[1 + (-1)bso_32] + i69[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) = [3]   
POL(LOAD1232(x1, x2, x3)) = x3 + [-1]x1   
POL(COND_LOAD1232(x1, x2, x3, x4)) = x4 + [-1]x2   
POL(&&(x1, x2)) = [-1]   
POL(<=(x1, x2)) = [-1]   
POL(COND_LOAD1222(x1, x2, x3, x4)) = [-1] + x3 + [-1]x2   
POL(LOAD1222(x1, x2, x3)) = [-1] + x2 + [-1]x1   
POL(>=(x1, x2)) = [-1]   
POL(0) = 0   
POL(>(x1, x2)) = [-1]   

The following pairs are in P>:

COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3])

The following pairs are in Pbound:

LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])
COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1])
LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])
COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3])

The following pairs are in P≥:

LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])
COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1])
LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])

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

(81) Complex Obligation (AND)

(82) Obligation:

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


The following domains are used:

Boolean, Integer


R is empty.

The integer pair graph contains the following rules and edges:
(2): LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(i85[2] <= i69[2] && i79[2] <= i69[2], i79[2], i85[2], i69[2])
(1): COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1])
(0): LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(i69[0] >= 0 && i85[0] > i69[0] && i79[0] <= i69[0], i79[0], i85[0], i69[0])

(0) -> (1), if ((i79[0] →* i79[1])∧(i85[0] →* i85[1])∧(i69[0] →* i69[1])∧(i69[0] >= 0 && i85[0] > i69[0] && i79[0] <= i69[0] →* TRUE))


(1) -> (2), if ((i79[1] →* i79[2])∧(i69[1] →* i69[2])∧(i85[1] →* i85[2]))



The set Q consists of the following terms:
Load1222(x0, x1, x2)
Cond_Load1222(TRUE, x0, x1, x2)
Load1232(x0, x1, x2)
Cond_Load1232(TRUE, x0, x1, x2)
Cond_Load12221(TRUE, x0, x1, x2)
Cond_Load12321(TRUE, x0, x1, x2)
Cond_Load12222(TRUE, x0, x1, x2)
Cond_Load12322(TRUE, x0, x1, x2)
Cond_Load12223(TRUE, x0, x1, x2)

(83) IDependencyGraphProof (EQUIVALENT transformation)

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

(84) TRUE

(85) Obligation:

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


The following domains are used:
none


R is empty.

The integer pair graph is empty.

The set Q consists of the following terms:
Load1222(x0, x1, x2)
Cond_Load1222(TRUE, x0, x1, x2)
Load1232(x0, x1, x2)
Cond_Load1232(TRUE, x0, x1, x2)
Cond_Load12221(TRUE, x0, x1, x2)
Cond_Load12321(TRUE, x0, x1, x2)
Cond_Load12222(TRUE, x0, x1, x2)
Cond_Load12322(TRUE, x0, x1, x2)
Cond_Load12223(TRUE, x0, x1, x2)

(86) IDependencyGraphProof (EQUIVALENT transformation)

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

(87) TRUE

(88) 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:
(3): COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3])
(2): LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(i85[2] <= i69[2] && i79[2] <= i69[2], i79[2], i85[2], i69[2])
(1): COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1])

(1) -> (2), if ((i79[1] →* i79[2])∧(i69[1] →* i69[2])∧(i85[1] →* i85[2]))


(2) -> (3), if ((i85[2] →* i85[3])∧(i69[2] →* i69[3])∧(i85[2] <= i69[2] && i79[2] <= i69[2] →* TRUE)∧(i79[2] →* i79[3]))



The set Q consists of the following terms:
Load1222(x0, x1, x2)
Cond_Load1222(TRUE, x0, x1, x2)
Load1232(x0, x1, x2)
Cond_Load1232(TRUE, x0, x1, x2)
Cond_Load12221(TRUE, x0, x1, x2)
Cond_Load12321(TRUE, x0, x1, x2)
Cond_Load12222(TRUE, x0, x1, x2)
Cond_Load12322(TRUE, x0, x1, x2)
Cond_Load12223(TRUE, x0, x1, x2)

(89) IDependencyGraphProof (EQUIVALENT transformation)

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

(90) TRUE