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:
|   TrackKey |   InvoiceDate |   CustomerKey |   EmployeeKey |   BillingKey |   unit_price |   quantity |   total |   Billing_id | BillingAddress                  | BillingCity         | BillingState   | BillingCountry   | BillingPostalCode   |   RowIsCurrent | RowStartDate            | RowEndDate              | RowChangeReason   |   Total | CurrentAge   |
|-----------:|--------------:|--------------:|--------------:|-------------:|-------------:|-----------:|--------:|-------------:|:--------------------------------|:--------------------|:---------------|:-----------------|:--------------------|---------------:|:------------------------|:------------------------|:------------------|--------:|:-------------|
|       1382 |      20120124 |            19 |             3 |          255 |         0.99 |          1 |    0.99 |          255 | 1 Infinite Loop                 | Cupertino           | CA             | USA              | 95014               |              1 | 1899-12-31 00:00:00.000 | 9999-12-31 00:00:00.000 |                   |    5.94 |              |
|        334 |      20121207 |             1 |             3 |          327 |         0.99 |          1 |    0.99 |          327 | Av. Brigadeiro Faria Lima, 2170 | São José dos Campos | SP             | Brazil           | 12227-000           |              1 | 1899-12-31 00:00:00.000 | 9999-12-31 00:00:00.000 |                   |   13.86 |              |
|       3253 |      20110621 |            48 |             5 |          206 |         0.99 |          1 |    0.99 |          206 | Lijnbaansgracht 120bg           | Amsterdam           | VV             | Netherlands      | 1016                |              1 | 1899-12-31 00:00:00.000 | 9999-12-31 00:00:00.000 |                   |    8.94 |              |
|       2362 |      20091112 |            40 |             4 |           74 |         0.99 |          1 |    0.99 |           74 | 8, Rue Hanovre                  | Paris               |                | France           | 75002               |              1 | 1899-12-31 00:00:00.000 | 9999-12-31 00:00:00.000 |                   |    8.91 |              |
|       1365 |      20130506 |             5 |             4 |          361 |         0.99 |          1 |    0.99 |          361 | Klanova 9/506                   | Prague              |                | Czech Republic   | 14700               |              1 | 1899-12-31 00:00:00.000 | 9999-12-31 00:00:00.000 |                   |    8.91 |              |
|       1594 |      20120224 |            57 |             5 |          262 |         0.99 |          1 |    0.99 |          262 | Calle Lira, 198                 | Santiago            |                | Chile            |                     |              1 | 1899-12-31 00:00:00.000 | 9999-12-31 00:00:00.000 |                   |    5.94 |              |
|        732 |      20090406 |             4 |             4 |           24 |         0.99 |          1 |    0.99 |           24 | Ullevålsveien 14                | Oslo                |                | Norway           | 0171                |              1 | 1899-12-31 00:00:00.000 | 9999-12-31 00:00:00.000 |                   |    5.94 |              |
|       1554 |      20130601 |            29 |             3 |          364 |         0.99 |          1 |    0.99 |          364 | 796 Dundas Street West          | Toronto             | ON             | Canada           | M6J 1V1             |              1 | 1899-12-31 00:00:00.000 | 9999-12-31 00:00:00.000 |                   |    1.98 |              |
|       2114 |      20120429 |            21 |             5 |          277 |         0.99 |          1 |    0.99 |          277 | 801 W 4th Street                | Reno                | NV             | USA              | 89503               |              1 | 1899-12-31 00:00:00.000 | 9999-12-31 00:00:00.000 |                   |    8.91 |              |
|        949 |      20130305 |            47 |             5 |          347 |         0.99 |          1 |    0.99 |          347 | Via Degli Scipioni, 43          | Rome                | RM             | Italy            | 00192               |              1 | 1899-12-31 00:00:00.000 | 9999-12-31 00:00:00.000 |                   |    8.91 |              |
|        706 |      20090405 |            59 |             3 |           23 |         0.99 |          1 |    0.99 |           23 | 3,Raj Bhavan Road               | Bangalore           |                | India            | 560001              |              1 | 1899-12-31 00:00:00.000 | 9999-12-31 00:00:00.000 |                   |    3.96 |              |
|       1120 |      20111223 |            36 |             5 |          247 |         0.99 |          1 |    0.99 |          247 | Tauentzienstraße 8              | Berlin              |                | Germany          | 10789               |              1 | 1899-12-31 00:00:00.000 | 9999-12-31 00:00:00.000 |                   |    3.96 |              |
|       3254 |      20100312 |             5 |             4 |          100 |         0.99 |          1 |    0.99 |          100 | Klanova 9/506                   | Prague              |                | Czech Republic   | 14700               |              1 | 1899-12-31 00:00:00.000 | 9999-12-31 00:00:00.000 |                   |    3.96 |              |
|        165 |      20121127 |            39 |             4 |          323 |         0.99 |          1 |    0.99 |          323 | 4, Rue Milton                   | Paris               |                | France           | 75009               |              1 | 1899-12-31 00:00:00.000 | 9999-12-31 00:00:00.000 |                   |    1.98 |              |
|       2341 |      20130907 |            39 |             4 |          389 |         0.99 |          1 |    0.99 |          389 | 4, Rue Milton                   | Paris               |                | France           | 75009               |              1 | 1899-12-31 00:00:00.000 | 9999-12-31 00:00:00.000 |                   |    8.91 |              |
|       2951 |      20131204 |            23 |             4 |          407 |         0.99 |          1 |    0.99 |          407 | 69 Salem Street                 | Boston              | MA             | USA              | 2113                |              1 | 1899-12-31 00:00:00.000 | 9999-12-31 00:00:00.000 |                   |    1.98 |              |
|       2504 |      20120612 |            23 |             4 |          286 |         0.99 |          1 |    0.99 |          286 | 69 Salem Street                 | Boston              | MA             | USA              | 2113                |              1 | 1899-12-31 00:00:00.000 | 9999-12-31 00:00:00.000 |                   |    0.99 |              |
|       2148 |      20091012 |             2 |             5 |           67 |         0.99 |          1 |    0.99 |           67 | Theodor-Heuss-Straße 34         | Stuttgart           |                | Germany          | 70174               |              1 | 1899-12-31 00:00:00.000 | 9999-12-31 00:00:00.000 |                   |    8.91 |              |
|       2607 |      20110323 |            58 |             3 |          186 |         0.99 |          1 |    0.99 |          186 | 12,Community Centre             | Delhi               |                | India            | 110017              |              1 | 1899-12-31 00:00:00.000 | 9999-12-31 00:00:00.000 |                   |    8.91 |              |
|       2936 |      20120805 |            26 |             4 |          299 |         0.99 |          1 |    0.99 |          299 | 2211 W Berry Street             | Fort Worth          | TX             | USA              | 76110               |              1 | 1899-12-31 00:00:00.000 | 9999-12-31 00:00:00.000 |                   |   23.86 |              |
|        460 |      20110925 |            50 |             5 |          228 |         0.99 |          1 |    0.99 |          228 | C/ San Bernardo 85              | Madrid              |                | Spain            | 28015               |              1 | 1899-12-31 00:00:00.000 | 9999-12-31 00:00:00.000 |                   |    8.91 |              |
|       1590 |      20120223 |            53 |             3 |          261 |         0.99 |          1 |    0.99 |          261 | 113 Lupus St                    | London              |                | United Kingdom   | SW1V 3EN            |              1 | 1899-12-31 00:00:00.000 | 9999-12-31 00:00:00.000 |                   |    3.96 |              |
|        869 |      20130301 |            37 |             3 |          345 |         0.99 |          1 |    0.99 |          345 | Berger Straße 10                | Frankfurt           |                | Germany          | 60316               |              1 | 1899-12-31 00:00:00.000 | 9999-12-31 00:00:00.000 |                   |    3.96 |              |
|       1905 |      20101220 |             3 |             3 |          165 |         0.99 |          1 |    0.99 |          165 | 1498 rue Bélanger               | Montréal            | QC             | Canada           | H2G 1A7             |              1 | 1899-12-31 00:00:00.000 | 9999-12-31 00:00:00.000 |                   |    8.91 |              |
|        245 |      20100514 |            26 |             4 |          115 |         0.99 |          1 |    0.99 |          115 | 2211 W Berry Street             | Fort Worth          | TX             | USA              | 76110               |              1 | 1899-12-31 00:00:00.000 | 9999-12-31 00:00:00.000 |                   |    5.94 |              |
|       2226 |      20130812 |            10 |             4 |          383 |         0.99 |          1 |    0.99 |          383 | Rua Dr. Falcão Filho, 155       | São Paulo           | SP             | Brazil           | 01007-010           |              1 | 1899-12-31 00:00:00.000 | 9999-12-31 00:00:00.000 |                   |   13.86 |              |
|       3123 |      20120905 |             5 |             4 |          306 |         0.99 |          1 |    0.99 |          306 | Klanova 9/506                   | Prague              |                | Czech Republic   | 14700               |              1 | 1899-12-31 00:00:00.000 | 9999-12-31 00:00:00.000 |                   |   16.86 |              |
|       1668 |      20120227 |             4 |             4 |          263 |         0.99 |          1 |    0.99 |          263 | Ullevålsveien 14                | Oslo                |                | Norway           | 0171                |              1 | 1899-12-31 00:00:00.000 | 9999-12-31 00:00:00.000 |                   |    8.91 |              |
|       1111 |      20130402 |            20 |             4 |          353 |         0.99 |          1 |    0.99 |          353 | 541 Del Medio Avenue            | Mountain View       | CA             | USA              | 94040-111           |              1 | 1899-12-31 00:00:00.000 | 9999-12-31 00:00:00.000 |                   |    5.94 |              |
|       1634 |      20090807 |            34 |             4 |           51 |         0.99 |          1 |    0.99 |           51 | Rua da Assunção 53              | Lisbon              |                | Portugal         |                     |              1 | 1899-12-31 00:00:00.000 | 9999-12-31 00:00:00.000 |                   |    3.96 |              |
|       2445 |      20120604 |             9 |             4 |          285 |         0.99 |          1 |    0.99 |          285 | Sønder Boulevard 51             | Copenhagen          |                | Denmark          | 1720                |              1 | 1899-12-31 00:00:00.000 | 9999-12-31 00:00:00.000 |                   |   13.86 |              |
|       2346 |      20120530 |            59 |             3 |          284 |         0.99 |          1 |    0.99 |          284 | 3,Raj Bhavan Road               | Bangalore           |                | India            | 560001              |              1 | 1899-12-31 00:00:00.000 | 9999-12-31 00:00:00.000 |                   |    8.91 |              |
|       3187 |      20100218 |            45 |             3 |           96 |         1.99 |          1 |    1.99 |           96 | Erzsébet krt. 58.               | Budapest            |                | Hungary          | H-1073              |              1 | 1899-12-31 00:00:00.000 | 9999-12-31 00:00:00.000 |                   |   21.86 |              |
|       1463 |      20120201 |            34 |             4 |          257 |         0.99 |          1 |    0.99 |          257 | Rua da Assunção 53              | Lisbon              |                | Portugal         |                     |              1 | 1899-12-31 00:00:00.000 | 9999-12-31 00:00:00.000 |                   |   13.86 |              |
|       2103 |      20130807 |             1 |             3 |          382 |         0.99 |          1 |    0.99 |          382 | Av. Brigadeiro Faria Lima, 2170 | São José dos Campos | SP             | Brazil           | 12227-000           |              1 | 1899-12-31 00:00:00.000 | 9999-12-31 00:00:00.000 |                   |    8.91 |              |
|        370 |      20121207 |             1 |             3 |          327 |         0.99 |          1 |    0.99 |          327 | Av. Brigadeiro Faria Lima, 2170 | São José dos Campos | SP             | Brazil           | 12227-000           |              1 | 1899-12-31 00:00:00.000 | 9999-12-31 00:00:00.000 |                   |   13.86 |              |
|       1176 |      20090607 |            21 |             5 |           38 |         0.99 |          1 |    0.99 |           38 | 801 W 4th Street                | Reno                | NV             | USA              | 89503               |              1 | 1899-12-31 00:00:00.000 | 9999-12-31 00:00:00.000 |                   |    5.94 |              |
|        237 |      20100514 |            26 |             4 |          115 |         0.99 |          1 |    0.99 |          115 | 2211 W Berry Street             | Fort Worth          | TX             | USA              | 76110               |              1 | 1899-12-31 00:00:00.000 | 9999-12-31 00:00:00.000 |                   |    5.94 |              |
|       2120 |      20091009 |            55 |             4 |           66 |         0.99 |          1 |    0.99 |           66 | 421 Bourke Street               | Sidney              | NSW            | Australia        | 2010                |              1 | 1899-12-31 00:00:00.000 | 9999-12-31 00:00:00.000 |                   |    5.94 |              |
|       2499 |      20131005 |            12 |             3 |          395 |         0.99 |          1 |    0.99 |          395 | Praça Pio X, 119                | Rio de Janeiro      | RJ             | Brazil           | 20040-020           |              1 | 1899-12-31 00:00:00.000 | 9999-12-31 00:00:00.000 |                   |    5.94 |              |
|       1103 |      20130401 |            16 |             4 |          352 |         0.99 |          1 |    0.99 |          352 | 1600 Amphitheatre Parkway       | Mountain View       | CA             | USA              | 94043-1351          |              1 | 1899-12-31 00:00:00.000 | 9999-12-31 00:00:00.000 |                   |    3.96 |              |
|       2272 |      20110125 |            50 |             5 |          173 |         0.99 |          1 |    0.99 |          173 | C/ San Bernardo 85              | Madrid              |                | Spain            | 28015               |              1 | 1899-12-31 00:00:00.000 | 9999-12-31 00:00:00.000 |                   |   13.86 |              |
|       2970 |      20120826 |            41 |             5 |          301 |         0.99 |          1 |    0.99 |          301 | 11, Place Bellecour             | Lyon                |                | France           | 69002               |              1 | 1899-12-31 00:00:00.000 | 9999-12-31 00:00:00.000 |                   |    1.98 |              |
|       2287 |      20130904 |            33 |             3 |          388 |         0.99 |          1 |    0.99 |          388 | 5112 48 Street                  | Yellowknife         | NT             | Canada           | X1A 1N6             |              1 | 1899-12-31 00:00:00.000 | 9999-12-31 00:00:00.000 |                   |    5.94 |              |
|       3284 |      20100313 |             9 |             4 |          101 |         0.99 |          1 |    0.99 |          101 | Sønder Boulevard 51             | Copenhagen          |                | Denmark          | 1720                |              1 | 1899-12-31 00:00:00.000 | 9999-12-31 00:00:00.000 |                   |    5.94 |              |
|       2794 |      20100109 |            47 |             5 |           86 |         0.99 |          1 |    0.99 |           86 | Via Degli Scipioni, 43          | Rome                | RM             | Italy            | 00192               |              1 | 1899-12-31 00:00:00.000 | 9999-12-31 00:00:00.000 |                   |    3.96 |              |
|       3369 |      20110629 |             4 |             4 |          208 |         0.99 |          1 |    0.99 |          208 | Ullevålsveien 14                | Oslo                |                | Norway           | 0171                |              1 | 1899-12-31 00:00:00.000 | 9999-12-31 00:00:00.000 |                   |   15.86 |              |
|        903 |      20090414 |            19 |             3 |           26 |         0.99 |          1 |    0.99 |           26 | 1 Infinite Loop                 | Cupertino           | CA             | USA              | 95014               |              1 | 1899-12-31 00:00:00.000 | 9999-12-31 00:00:00.000 |                   |   13.86 |              |
|       2714 |      20091218 |            28 |             5 |           82 |         0.99 |          1 |    0.99 |           82 | 302 S 700 E                     | Salt Lake City      | UT             | USA              | 84102               |              1 | 1899-12-31 00:00:00.000 | 9999-12-31 00:00:00.000 |                   |   13.86 |              |
|        153 |      20090111 |            23 |             4 |            5 |         0.99 |          1 |    0.99 |            5 | 69 Salem Street                 | Boston              | MA             | USA              | 2113                |              1 | 1899-12-31 00:00:00.000 | 9999-12-31 00:00:00.000 |                   |   13.86 |              |



label: BillingKey
Billing_id
BillingKey
BillingAddress
BillingKey
BillingCity
BillingKey
BillingState
BillingKey
BillingCountry
BillingKey
BillingPostalCode
BillingKey
RowIsCurrent
BillingKey
RowStartDate
BillingKey
RowEndDate
BillingKey
Total
output: {"Functional-Dependency": [["BillingKey", "Billing_id"], ["BillingKey", "BillingAddress"], ["BillingKey", "BillingCity"], ["BillingKey", "BillingState"], ["BillingKey", "BillingCountry"], ["BillingKey", "BillingPostalCode"], ["BillingKey", "RowIsCurrent"], ["BillingKey", "RowStartDate"], ["BillingKey", "RowEndDate"], ["BillingKey", "Total"]]}
labeled_fds: BillingKey
Billing_id
BillingKey
BillingAddress
BillingKey
BillingCity
BillingKey
BillingState
BillingKey
BillingCountry
BillingKey
BillingPostalCode
BillingKey
RowIsCurrent
BillingKey
RowStartDate
BillingKey
RowEndDate
BillingKey
Total
TrackKey
InvoiceDate
TrackKey
CustomerKey
TrackKey
EmployeeKey
TrackKey
BillingState
TrackKey
BillingPostalCode
TrackKey
Total
InvoiceDate
CustomerKey
InvoiceDate
EmployeeKey
InvoiceDate
unit_price
InvoiceDate
total
InvoiceDate
Billing_id
InvoiceDate
BillingAddress
InvoiceDate
BillingCity
InvoiceDate
BillingState
InvoiceDate
BillingCountry
InvoiceDate
BillingPostalCode
InvoiceDate
Total
BillingKey
unit_price
BillingKey
total
Billing_id
unit_price
source: $MMTU_HOME/resources/Relationship-finding/FD/179203299