Task: Functional-Dependency (source dataset: Auto-Relate)

Given a table represented shown below, your task is to determine functional dependencies that exist in the table. Recall that a functional dependency is a relationship where the value of one attribute (or a set of attributes), known as the determinant columns, can uniquely determines the value of another attribute, known as the dependent columns (e.g., student-ID => student-Name, car-model => car-make, employee-ID => department, etc.).

Instructions:
Analyze the provided table below, identify all functional dependencies that should semantically hold in the table. Do not produce spurious relationships that not semantically meaningful.

No explanation, format the output as a JSON object:{"Functional-Dependency": <list of functional dependencies>}. Each functional dependency should be represented as [<determinant column>, <dependent column>]

Input Table:
|   ProdutoID | Produto               |   Quantidade |   Valor |   CupomID |   Lucro | EmpresaFrete    | Data                    | DataEntrega             |   TempoEntrega |
|------------:|:----------------------|-------------:|--------:|----------:|--------:|:----------------|:------------------------|:------------------------|---------------:|
|          29 | Davenport             |           60 |  917025 |     10912 |  269972 | One Liners      | 2017-11-29 00:00:00.000 | 2017-12-16 00:00:00.000 |             17 |
|          41 | Duck Shirt            |           30 |   28319 |     10769 |    6473 | One Liners      | 2017-03-13 00:00:00.000 | 2017-03-29 00:00:00.000 |             16 |
|          14 | Kool Sunglasses       |           35 |   85155 |     10427 |   14465 | Ship for U      | 2015-10-01 00:00:00.000 | 2015-10-08 00:00:00.000 |              7 |
|          60 | Game Over T-Shirt     |           15 |    7995 |     10728 |    1519 | One Liners      | 2017-02-05 00:00:00.000 | 2017-02-09 00:00:00.000 |              4 |
|          40 | Duck Trousers         |           40 |   87824 |     11063 |   17405 | One Liners      | 2017-08-05 00:00:00.000 | 2017-08-15 00:00:00.000 |             10 |
|           5 | O-Man Underwear       |           30 |    1848 |     10848 |    2181 | One Liners      | 2018-02-26 00:00:00.000 | 2018-03-11 00:00:00.000 |             13 |
|          52 | Small Crocodile Boots |           15 |  126654 |     10446 |   31318 | Freight Express | 2015-06-19 00:00:00.000 | 2015-07-04 00:00:00.000 |             15 |
|          75 | Bow tie               |           42 |    3528 |     10786 |   11466 | One Liners      | 2017-03-24 00:00:00.000 | 2017-04-11 00:00:00.000 |             18 |
|          71 | Atles Lussekofta      |            2 |    5952 |     10304 |     809 | Freight Express | 2016-07-17 00:00:00.000 | 2016-08-01 00:00:00.000 |             15 |
|          59 | Rasta WCT             |           30 |    2478 |     11036 |    2924 | One Liners      | 2017-08-26 00:00:00.000 | 2017-08-30 00:00:00.000 |              4 |
|          45 | Danske Treshoe        |           21 |    2100 |     10502 |    3612 | One Liners      | 2015-09-14 00:00:00.000 | 2015-09-15 00:00:00.000 |              1 |
|          55 | Feiss Fleece Trousers |           12 |   44453 |     10630 |    8986 | One Liners      | 2016-12-16 00:00:00.000 | 2016-12-31 00:00:00.000 |             15 |
|          31 | Rossi Bermuda Shorts  |            3 |    2729 |     10446 |     675 | Freight Express | 2015-06-19 00:00:00.000 | 2015-07-04 00:00:00.000 |             15 |
|          55 | Feiss Fleece Trousers |          120 |  528396 |     10451 |  130658 | One Liners      | 2016-03-25 00:00:00.000 | 2016-04-09 00:00:00.000 |             15 |
|           1 | Lenin Jeansshorts     |           15 |   33482 |     10348 |    8327 | One Liners      | 2017-08-13 00:00:00.000 | 2017-08-26 00:00:00.000 |             13 |
|          70 | US-Master Jeans       |           30 |    8832 |     10885 |   10422 | Ship for U      | 2017-11-15 00:00:00.000 | 2017-11-16 00:00:00.000 |              1 |
|          61 | Adihash Running Shoe  |           16 |    3888 |     10418 |    6687 | One Liners      | 2016-04-22 00:00:00.000 | 2016-05-06 00:00:00.000 |             14 |
|          52 | Small Crocodile Boots |            6 |   46727 |     10961 |    7476 | One Liners      | 2017-06-24 00:00:00.000 | 2017-07-06 00:00:00.000 |             12 |
|          45 | Danske Treshoe        |           40 |   40572 |     10750 |   11995 | One Liners      | 2016-07-26 00:00:00.000 | 2016-07-30 00:00:00.000 |              4 |
|          67 | X-Dress               |           30 |   18996 |     10502 |   32673 | One Liners      | 2015-09-14 00:00:00.000 | 2015-09-15 00:00:00.000 |              1 |
|          26 | Bike Helmet           |           12 |   40128 |     11024 |    4735 | One Liners      | 2017-07-21 00:00:00.000 | 2017-07-23 00:00:00.000 |              2 |
|          18 | Deuce shirt           |           12 |   40845 |     10719 |   14377 | Freight Express | 2017-01-29 00:00:00.000 | 2017-02-11 00:00:00.000 |             13 |
|          21 | Basket Shoes          |            8 |    8736 |     10614 |     166 | One Liners      | 2016-11-01 00:00:00.000 | 2016-11-03 00:00:00.000 |              2 |
|          10 | Sapporoo Gloves       |           20 |    1506 |     10685 |    2861 | One Liners      | 2017-03-03 00:00:00.000 | 2017-03-14 00:00:00.000 |             11 |
|          64 | WFS shoes             |            8 |   27912 |     10957 |    3294 | One Liners      | 2017-08-24 00:00:00.000 | 2017-08-25 00:00:00.000 |              1 |
|          12 | Tiny Winy Hot Bikini  |           36 |   40324 |     10633 |   11922 | Ship for U      | 2016-07-20 00:00:00.000 | 2016-07-28 00:00:00.000 |              8 |
|          77 | Skirt                 |           20 |    2752 |     10812 |    5229 | One Liners      | 2017-08-08 00:00:00.000 | 2017-08-28 00:00:00.000 |             20 |
|          16 | Wimbledon T-Shirt     |           30 |   31317 |     10932 |    4952 | Freight Express | 2017-08-12 00:00:00.000 | 2017-08-17 00:00:00.000 |              5 |
|          60 | Game Over T-Shirt     |           40 |    1828 |     10612 |    3473 | One Liners      | 2016-07-02 00:00:00.000 | 2016-07-09 00:00:00.000 |              7 |
|          75 | Bow tie               |           30 |    2307 |     10998 |    2722 | One Liners      | 2017-07-08 00:00:00.000 | 2017-07-15 00:00:00.000 |              7 |
|          76 | Minnki PÃ¤lsii        |           20 |   82500 |     10732 |   15675 | One Liners      | 2017-02-08 00:00:00.000 | 2017-02-24 00:00:00.000 |             16 |
|          37 | Mehmet-Skor           |            7 |     315 |     11083 |     372 | Ship for U      | 2017-02-22 00:00:00.000 | 2017-03-08 00:00:00.000 |             14 |
|          14 | Kool Sunglasses       |           50 |  127411 |     11077 |   18308 | One Liners      | 2018-03-11 00:00:00.000 | 2018-03-22 00:00:00.000 |             11 |
|          26 | Bike Helmet           |           30 |    8463 |     10458 |   14556 | One Liners      | 2017-08-01 00:00:00.000 | 2017-08-06 00:00:00.000 |              5 |
|          37 | Mehmet-Skor           |            1 |     437 |     10259 |      59 | One Liners      | 2015-10-23 00:00:00.000 | 2015-11-01 00:00:00.000 |              9 |
|          62 | Sheat Shoes           |           14 |   41642 |     10932 |    7893 | Freight Express | 2017-08-12 00:00:00.000 | 2017-08-17 00:00:00.000 |              5 |
|          71 | Atles Lussekofta      |           12 |   39144 |     10473 |    6733 | One Liners      | 2015-06-18 00:00:00.000 | 2015-06-23 00:00:00.000 |              5 |
|           2 | Mr X Trousers         |           25 |    5766 |     10327 |   16145 | One Liners      | 2015-03-17 00:00:00.000 | 2015-03-28 00:00:00.000 |             11 |
|          41 | Duck Shirt            |           28 |   31354 |     11014 |    6214 | One Liners      | 2017-07-16 00:00:00.000 | 2017-07-18 00:00:00.000 |              2 |
|          77 | Skirt                 |           10 |    1198 |     11077 |    1414 | One Liners      | 2018-03-11 00:00:00.000 | 2018-03-22 00:00:00.000 |             11 |
|          42 | Balett Shoes          |          100 |   16692 |     10588 |   54249 | One Liners      | 2016-10-05 00:00:00.000 | 2016-10-16 00:00:00.000 |             11 |
|          20 | Tennis Suit           |            5 |    4107 |     10927 |    4846 | Ship for U      | 2017-12-09 00:00:00.000 | 2017-12-16 00:00:00.000 |              7 |
|          43 | Summer Shorts         |            5 |    5545 |     10842 |     654 | Freight Express | 2017-10-24 00:00:00.000 | 2017-11-06 00:00:00.000 |             13 |
|          67 | X-Dress               |            3 |   17103 |     10775 |     325 | One Liners      | 2017-03-17 00:00:00.000 | 2017-03-18 00:00:00.000 |              1 |
|          72 | Rossi Shorts          |           40 |    4384 |     10325 |    5962 | One Liners      | 2015-08-15 00:00:00.000 | 2015-08-24 00:00:00.000 |              9 |
|          40 | Duck Trousers         |           10 |    1678 |     11003 |     198 | One Liners      | 2017-07-12 00:00:00.000 | 2017-07-25 00:00:00.000 |             13 |
|          13 | Aino Shoes            |            3 |    9216 |     10832 |    2442 | Ship for U      | 2017-04-18 00:00:00.000 | 2017-04-19 00:00:00.000 |              1 |
|          75 | Bow tie               |           25 |    1845 |     10670 |    3506 | One Liners      | 2016-12-19 00:00:00.000 | 2016-12-22 00:00:00.000 |              3 |
|          49 | Finnish Sport Blades  |           18 |    3240 |     10612 |    6156 | One Liners      | 2016-07-02 00:00:00.000 | 2016-07-09 00:00:00.000 |              7 |
|          24 | Samba Socker  Socks   |           10 |    4968 |     11051 |    1317 | One Liners      | 2017-08-02 00:00:00.000 | 2017-08-20 00:00:00.000 |             18 |



label: CupomID
EmpresaFrete
CupomID
Data
CupomID
DataEntrega
CupomID
TempoEntrega
output: {"Functional-Dependency": [["CupomID", "EmpresaFrete"], ["CupomID", "Data"], ["CupomID", "DataEntrega"], ["CupomID", "TempoEntrega"]]}
labeled_fds: CupomID
EmpresaFrete
CupomID
Data
CupomID
DataEntrega
CupomID
TempoEntrega
Valor
ProdutoID
Valor
Produto
Valor
CupomID
Valor
Lucro
Valor
EmpresaFrete
Valor
Data
Valor
TempoEntrega
Lucro
ProdutoID
Lucro
Produto
Lucro
Quantidade
Lucro
Valor
Lucro
EmpresaFrete
Lucro
Data
Lucro
DataEntrega
Lucro
TempoEntrega
source: $MMTU_HOME/resources/Relationship-finding/FD/886260833