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:
|   cart_id |   customer_id |   order_id |   invoice_id |   stage_id |   source_id | Stage Name       | Sorted Stage       |
|----------:|--------------:|-----------:|-------------:|-----------:|------------:|:-----------------|:-------------------|
|       550 |            80 |       1139 |          293 |          1 |           5 | Shopping         | 1 Shopping         |
|        64 |           577 |        700 |          202 |          3 |           4 | Add Address      | 3 Add Address      |
|        96 |           250 |       1045 |         1757 |          3 |           7 | Add Address      | 3 Add Address      |
|       595 |           175 |       1156 |         1615 |          2 |           3 | Start Checkout   | 2 Start Checkout   |
|        49 |           880 |       1098 |         1444 |          1 |           6 | Shopping         | 1 Shopping         |
|       669 |           630 |       1603 |          621 |          2 |           3 | Start Checkout   | 2 Start Checkout   |
|       432 |           274 |       1380 |          919 |          2 |           2 | Start Checkout   | 2 Start Checkout   |
|       440 |           705 |       1591 |         1505 |          1 |           5 | Shopping         | 1 Shopping         |
|       357 |           997 |       1497 |          840 |          4 |           5 | Add Payment      | 4 Add Payment      |
|       489 |            13 |       1701 |         1727 |          1 |           3 | Shopping         | 1 Shopping         |
|       779 |           921 |        882 |          735 |          3 |           5 | Add Address      | 3 Add Address      |
|       872 |           647 |        651 |         1161 |          1 |           7 | Shopping         | 1 Shopping         |
|       494 |           648 |        448 |          913 |          2 |           2 | Start Checkout   | 2 Start Checkout   |
|       748 |           586 |        822 |          116 |          7 |           7 | Shipped          | 7 Shipped          |
|       235 |           186 |         12 |         1633 |          7 |           4 | Shipped          | 7 Shipped          |
|       874 |           547 |        583 |         1756 |          4 |           4 | Add Payment      | 4 Add Payment      |
|       379 |           383 |       1983 |         1439 |          1 |           1 | Shopping         | 1 Shopping         |
|       675 |           431 |        891 |         1991 |          4 |           4 | Add Payment      | 4 Add Payment      |
|       299 |           473 |       1926 |          125 |          3 |           1 | Add Address      | 3 Add Address      |
|       805 |           281 |       1653 |          119 |          1 |           1 | Shopping         | 1 Shopping         |
|       945 |           356 |       1637 |         1005 |          1 |           5 | Shopping         | 1 Shopping         |
|       981 |           540 |       1793 |         1785 |          1 |           3 | Shopping         | 1 Shopping         |
|       526 |           405 |        162 |         1956 |          1 |           4 | Shopping         | 1 Shopping         |
|       678 |           680 |       1123 |          900 |          1 |           5 | Shopping         | 1 Shopping         |
|       430 |           545 |        709 |          808 |          1 |           2 | Shopping         | 1 Shopping         |
|       743 |           821 |       1670 |         1381 |          1 |           2 | Shopping         | 1 Shopping         |
|       163 |           433 |       1626 |         1232 |          1 |           3 | Shopping         | 1 Shopping         |
|       884 |           984 |       1963 |          786 |          5 |           3 | Order Created    | 5 Order Created    |
|       899 |           863 |       1157 |          377 |          4 |           5 | Add Payment      | 4 Add Payment      |
|       358 |           533 |       1735 |          974 |          6 |           6 | Order Processing | 6 Order Processing |
|       159 |           258 |        786 |          629 |          1 |           4 | Shopping         | 1 Shopping         |
|       556 |           764 |       1548 |          916 |          1 |           3 | Shopping         | 1 Shopping         |
|       407 |            38 |        126 |          170 |          2 |           4 | Start Checkout   | 2 Start Checkout   |
|       290 |           366 |        570 |          544 |          1 |           5 | Shopping         | 1 Shopping         |
|       523 |           803 |       1371 |         1784 |          1 |           4 | Shopping         | 1 Shopping         |
|       314 |           693 |        149 |          565 |          1 |           2 | Shopping         | 1 Shopping         |
|       721 |           903 |       1271 |          484 |          2 |           1 | Start Checkout   | 2 Start Checkout   |
|       179 |           848 |       1235 |         1252 |          2 |           6 | Start Checkout   | 2 Start Checkout   |
|       895 |            32 |       1564 |          997 |          4 |           6 | Add Payment      | 4 Add Payment      |
|       700 |           698 |        885 |         1491 |          1 |           7 | Shopping         | 1 Shopping         |
|       936 |            28 |        272 |         1616 |          1 |           1 | Shopping         | 1 Shopping         |
|       118 |           924 |        236 |         1690 |          1 |           3 | Shopping         | 1 Shopping         |
|       711 |           670 |       1650 |          443 |          1 |           1 | Shopping         | 1 Shopping         |
|       761 |           921 |        625 |          827 |          7 |           2 | Shipped          | 7 Shipped          |
|       585 |           913 |       1930 |          659 |          1 |           1 | Shopping         | 1 Shopping         |
|       318 |           263 |        435 |         1092 |          1 |           1 | Shopping         | 1 Shopping         |
|       122 |           477 |        585 |         1271 |          5 |           4 | Order Created    | 5 Order Created    |
|       285 |            13 |        651 |         1402 |          2 |           1 | Start Checkout   | 2 Start Checkout   |
|       389 |           419 |       1277 |          897 |          1 |           6 | Shopping         | 1 Shopping         |
|        48 |           951 |         34 |         1716 |          4 |           4 | Add Payment      | 4 Add Payment      |



label: stage_id
Stage Name
stage_id
Sorted Stage
output: {"Functional-Dependency": [["stage_id", "Stage Name"], ["stage_id", "Sorted Stage"]]}
labeled_fds: stage_id
Stage Name
stage_id
Sorted Stage
order_id
Sorted Stage
source: $MMTU_HOME/resources/Relationship-finding/FD/168309358