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:
|   Peça |   Máquina | Data e Hora             | Produto   |   Lote |   Comprimento (mm) |   Espessura (mm) | Status   | Causa_defeito           |   Status_num |   Hour |   Comprimento LI |   Comprimento LS |   Espessura LI |   Espessura LS |
|-------:|----------:|:------------------------|:----------|-------:|-------------------:|-----------------:|:---------|:------------------------|-------------:|-------:|-----------------:|-----------------:|---------------:|---------------:|
|     38 |         1 | 2018-01-13 01:37:00.000 | A         |     24 |            4.65    |         0.860465 | OK       |                         |            0 |      1 |              4.2 |              5   |           0.75 |           0.95 |
|     48 |         3 | 2018-01-10 17:31:00.000 | A         |     13 |            4.53906 |         0.850187 | OK       |                         |            0 |     17 |              4.2 |              5   |           0.75 |           0.95 |
|      6 |         2 | 2018-01-12 03:09:00.000 | B         |     21 |            4.02752 |         0.647727 | OK       |                         |            0 |      3 |              3.7 |              4.3 |           0.5  |           0.9  |
|     60 |         3 | 2018-01-13 16:23:00.000 | B         |     34 |            3.74545 |         0.748466 | OK       |                         |            0 |     16 |              3.7 |              4.3 |           0.5  |           0.9  |
|     79 |         2 | 2018-01-11 14:29:00.000 | B         |     18 |            4.14851 |         0.781457 | OK       |                         |            0 |     14 |              3.7 |              4.3 |           0.5  |           0.9  |
|     79 |         1 | 2018-01-10 11:55:00.000 | A         |     10 |            4.36047 |         0.944882 | OK       |                         |            0 |     11 |              4.2 |              5   |           0.75 |           0.95 |
|     44 |         1 | 2018-01-13 17:04:00.000 | A         |     27 |            4.33333 |         0.804688 | OK       |                         |            0 |     17 |              4.2 |              5   |           0.75 |           0.95 |
|     69 |         2 | 2018-01-12 19:21:00.000 | B         |     23 |            3.62162 |         0.60479  | Refugo   | Lâmina                  |            1 |     19 |              3.7 |              4.3 |           0.5  |           0.9  |
|     21 |         3 | 2018-01-12 09:13:00.000 | B         |     26 |            3.62832 |         0.793548 | Refugo   | Lâmina                  |            1 |      9 |              3.7 |              4.3 |           0.5  |           0.9  |
|     23 |         1 | 2018-01-12 02:13:00.000 | B         |     19 |            4.0396  |         0.810606 | OK       |                         |            0 |      2 |              3.7 |              4.3 |           0.5  |           0.9  |
|     16 |         3 | 2018-01-11 20:41:00.000 | B         |     22 |            3.59292 |         0.672316 | Refugo   | Temperatura de processo |            1 |     20 |              3.7 |              4.3 |           0.5  |           0.9  |
|     44 |         3 | 2018-01-13 19:35:00.000 | B         |     35 |            3.61261 |         0.70068  | Refugo   | Desalinhamento          |            1 |     19 |              3.7 |              4.3 |           0.5  |           0.9  |
|     47 |         2 | 2018-01-13 01:17:00.000 | B         |     24 |            3.80189 |         0.795775 | OK       |                         |            0 |      1 |              3.7 |              4.3 |           0.5  |           0.9  |
|     50 |         3 | 2018-01-12 21:23:00.000 | B         |     29 |            3.61947 |         0.798742 | Refugo   | Desalinhamento          |            1 |     21 |              3.7 |              4.3 |           0.5  |           0.9  |
|     60 |         3 | 2018-01-11 15:51:00.000 | B         |     20 |            4.09524 |         0.810127 | OK       |                         |            0 |     15 |              3.7 |              4.3 |           0.5  |           0.9  |
|     95 |         3 | 2018-01-11 11:11:00.000 | B         |     18 |            4.19048 |         0.682353 | OK       |                         |            0 |     11 |              3.7 |              4.3 |           0.5  |           0.9  |
|     45 |         2 | 2018-01-12 12:29:00.000 | B         |     22 |            3.76786 |         0.765957 | OK       |                         |            0 |     12 |              3.7 |              4.3 |           0.5  |           0.9  |
|     77 |         1 | 2018-01-14 03:46:00.000 | A         |     29 |            4.84091 |         0.924242 | OK       |                         |            0 |      3 |              4.2 |              5   |           0.75 |           0.95 |
|     85 |         1 | 2018-01-12 13:25:00.000 | A         |     21 |            5.05929 |         0.936255 | Refugo   | Temperatura de processo |            1 |     13 |              4.2 |              5   |           0.75 |           0.95 |
|     15 |         1 | 2018-01-14 00:40:00.000 | A         |     29 |            4.47126 |         0.782946 | OK       |                         |            0 |      0 |              4.2 |              5   |           0.75 |           0.95 |
|     87 |         2 | 2018-01-10 20:05:00.000 | B         |     15 |            4.04587 |         0.778481 | OK       |                         |            0 |     20 |              3.7 |              4.3 |           0.5  |           0.9  |
|     17 |         3 | 2018-01-10 16:29:00.000 | A         |     13 |            4.93023 |         0.849624 | OK       |                         |            0 |     16 |              4.2 |              5   |           0.75 |           0.95 |
|     17 |         3 | 2018-01-13 03:45:00.000 | B         |     31 |            3.81308 |         0.662577 | OK       |                         |            0 |      3 |              3.7 |              4.3 |           0.5  |           0.9  |
|     58 |         2 | 2018-01-12 18:37:00.000 | B         |     23 |            3.9375  |         0.884892 | OK       |                         |            0 |     18 |              3.7 |              4.3 |           0.5  |           0.9  |
|     37 |         2 | 2018-01-10 16:45:00.000 | B         |     15 |            3.85714 |         0.815385 | OK       |                         |            0 |     16 |              3.7 |              4.3 |           0.5  |           0.9  |
|     13 |         1 | 2018-01-10 08:37:00.000 | A         |     10 |            4.796   |         0.849624 | OK       |                         |            0 |      8 |              4.2 |              5   |           0.75 |           0.95 |
|     74 |         1 | 2018-01-13 21:34:00.000 | A         |     28 |            4.77011 |         0.854406 | OK       |                         |            0 |     21 |              4.2 |              5   |           0.75 |           0.95 |
|     17 |         3 | 2018-01-11 14:25:00.000 | B         |     20 |            3.61607 |         0.984733 | Refugo   | Desalinhamento          |            1 |     14 |              3.7 |              4.3 |           0.5  |           0.9  |
|     52 |         2 | 2018-01-10 17:45:00.000 | B         |     15 |            3.88785 |         0.816901 | OK       |                         |            0 |     17 |              3.7 |              4.3 |           0.5  |           0.9  |
|     12 |         2 | 2018-01-13 13:17:00.000 | B         |     26 |            4.33333 |         0.795918 | Refugo   | Lâmina                  |            1 |     13 |              3.7 |              4.3 |           0.5  |           0.9  |
|     36 |         2 | 2018-01-13 20:45:00.000 | B         |     27 |            3.90826 |         0.751553 | OK       |                         |            0 |     20 |              3.7 |              4.3 |           0.5  |           0.9  |
|     20 |         1 | 2018-01-11 12:37:00.000 | A         |     16 |            4.51894 |         0.828358 | OK       |                         |            0 |     12 |              4.2 |              5   |           0.75 |           0.95 |
|     37 |         1 | 2018-01-10 21:43:00.000 | A         |     13 |            4.94922 |         0.802974 | OK       |                         |            0 |     21 |              4.2 |              5   |           0.75 |           0.95 |
|     98 |         1 | 2018-01-13 22:46:00.000 | A         |     28 |            4.64143 |         0.800766 | OK       |                         |            0 |     22 |              4.2 |              5   |           0.75 |           0.95 |
|     78 |         3 | 2018-01-13 20:43:00.000 | B         |     35 |            4.35644 |         0.847682 | Refugo   | Desalinhamento          |            1 |     20 |              3.7 |              4.3 |           0.5  |           0.9  |
|      7 |         3 | 2018-01-10 19:01:00.000 | A         |     14 |            4.49412 |         0.84     | OK       |                         |            0 |     19 |              4.2 |              5   |           0.75 |           0.95 |
|     54 |         3 | 2018-01-10 17:43:00.000 | A         |     13 |            4.95019 |         0.952569 | Refugo   | Matéria prima           |            1 |     17 |              4.2 |              5   |           0.75 |           0.95 |
|     89 |         1 | 2018-01-13 09:43:00.000 | A         |     25 |            4.61508 |         0.825095 | OK       |                         |            0 |      9 |              4.2 |              5   |           0.75 |           0.95 |
|      1 |         2 | 2018-01-13 12:33:00.000 | B         |     26 |            4.25743 |         0.753165 | OK       |                         |            0 |     12 |              3.7 |              4.3 |           0.5  |           0.9  |
|     61 |         3 | 2018-01-13 05:13:00.000 | B         |     31 |            4.02885 |         0.740964 | OK       |                         |            0 |      5 |              3.7 |              4.3 |           0.5  |           0.9  |
|     10 |         3 | 2018-01-12 12:35:00.000 | B         |     27 |            3.98058 |         0.75     | OK       |                         |            0 |     12 |              3.7 |              4.3 |           0.5  |           0.9  |
|     47 |         1 | 2018-01-12 20:31:00.000 | A         |     23 |            5.088   |         0.855556 | Refugo   | Velocidade da máquina   |            1 |     20 |              4.2 |              5   |           0.75 |           0.95 |
|     26 |         2 | 2018-01-13 14:13:00.000 | B         |     26 |            4.21359 |         0.866197 | OK       |                         |            0 |     14 |              3.7 |              4.3 |           0.5  |           0.9  |
|     55 |         3 | 2018-01-11 15:41:00.000 | B         |     20 |            4.02857 |         0.860294 | OK       |                         |            0 |     15 |              3.7 |              4.3 |           0.5  |           0.9  |
|     12 |         3 | 2018-01-11 20:33:00.000 | B         |     22 |            3.80556 |         0.759259 | OK       |                         |            0 |     20 |              3.7 |              4.3 |           0.5  |           0.9  |
|     26 |         3 | 2018-01-10 12:11:00.000 | A         |     11 |            4.79762 |         0.901186 | OK       |                         |            0 |     12 |              4.2 |              5   |           0.75 |           0.95 |
|     34 |         3 | 2018-01-10 17:03:00.000 | A         |     13 |            4.52091 |         0.889328 | OK       |                         |            0 |     17 |              4.2 |              5   |           0.75 |           0.95 |
|     83 |         3 | 2018-01-12 22:29:00.000 | B         |     29 |            4.18269 |         0.802548 | OK       |                         |            0 |     22 |              3.7 |              4.3 |           0.5  |           0.9  |
|     48 |         1 | 2018-01-13 02:07:00.000 | A         |     24 |            4.79104 |         0.893939 | OK       |                         |            0 |      2 |              4.2 |              5   |           0.75 |           0.95 |
|     18 |         1 | 2018-01-11 01:04:00.000 | A         |     14 |            4.44706 |         0.864    | OK       |                         |            0 |      1 |              4.2 |              5   |           0.75 |           0.95 |



label: Produto
Comprimento LI
Produto
Comprimento LS
Produto
Espessura LI
Produto
Espessura LS
output: {"Functional-Dependency": [["Produto", "Comprimento LI"], ["Produto", "Comprimento LS"], ["Produto", "Espessura LI"], ["Produto", "Espessura LS"]]}
labeled_fds: Produto
Comprimento LI
Produto
Comprimento LS
Produto
Espessura LI
Produto
Espessura LS
Data e Hora
Lote
Data e Hora
Comprimento (mm)
Data e Hora
Espessura (mm)
Data e Hora
Status
Data e Hora
Causa_defeito
Data e Hora
Comprimento LI
Data e Hora
Comprimento LS
Data e Hora
Espessura LI
Comprimento (mm)
Produto
Comprimento (mm)
Espessura (mm)
Comprimento (mm)
Status
Comprimento (mm)
Causa_defeito
Comprimento (mm)
Status_num
Comprimento (mm)
Comprimento LI
Comprimento (mm)
Comprimento LS
Comprimento (mm)
Espessura LI
Comprimento (mm)
Espessura LS
Espessura (mm)
Máquina
Espessura (mm)
Produto
Espessura (mm)
Status
Espessura (mm)
Causa_defeito
Espessura (mm)
Status_num
Espessura (mm)
Comprimento LS
Espessura (mm)
Espessura LI
Espessura (mm)
Espessura LS
source: $MMTU_HOME/resources/Relationship-finding/FD/313692383