Task: Arithmetic-Relationship (source dataset: Auto-Relate)

You are given a table with numerical values in multiple columns. Your task is to analyze the data and identify semantic relationships, expressed in arithmetic relationships, that exist between columns.

These relationships may involve any combination of the following operations: addition (+), subtraction (−), multiplication (*), and division (/). The expressions can involve two or more columns and may be nested (e.g., B = (A + C) / D).

Please only identify arithmetic relationships that hold semantically based on the data, and do not return relationships that are likely spurious, e.g., (A = B * 0), where A is an all 0 column. Please only return minimal atomic relationships, e.g., if A = B + C and D = E + F, then there is no need to return A = B + C + E + F - D.

No explanation, return all the formula(s) in JSON format: {"Arithmetic-Relationship": [<list-of-formulas>]}. If no relationship is found, return {"Arithmetic-Relationship": []}.

Input Table:
|    A |   B |   C |   D |   E |   F |   G |   H |   I |   J |   K |   L |   M |    N |   O |    P |   Q |   R |
|-----:|----:|----:|----:|----:|----:|----:|----:|----:|----:|----:|----:|----:|-----:|----:|-----:|----:|----:|
| 1990 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 | 0.2 |   0 | 0.02 |   0 | 0.01 |   0 |   0 |
| 1991 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 | 0.2 |   0 | 0.02 |   0 | 0.01 |   0 |   0 |
| 1992 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 | 0.2 |   0 | 0.02 |   0 | 0.01 |   0 |   0 |
| 1993 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 | 0.2 |   0 | 0.02 |   0 | 0.01 |   0 |   0 |
| 1994 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 | 0.2 |   0 | 0.02 |   0 | 0.01 |   0 |   0 |
| 1995 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 | 0.2 |   0 | 0.02 |   0 | 0.01 |   0 |   0 |
| 1996 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 | 0.2 |   0 | 0.02 |   0 | 0.01 |   0 |   0 |
| 1997 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 | 0.2 |   0 | 0.02 |   0 | 0.01 |   0 |   0 |
| 1998 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 | 0.2 |   0 | 0.02 |   0 | 0.01 |   0 |   0 |
| 1999 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 | 0.2 |   0 | 0.02 |   0 | 0.01 |   0 |   0 |
| 2000 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 | 0.2 |   0 | 0.02 |   0 | 0.01 |   0 |   0 |
| 2001 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 | 0.2 |   0 | 0.02 |   0 | 0.01 |   0 |   0 |
| 2002 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 | 0.2 |   0 | 0.02 |   0 | 0.01 |   0 |   0 |
| 2003 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 | 0.2 |   0 | 0.02 |   0 | 0.01 |   0 |   0 |
| 2004 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 | 0.2 |   0 | 0.02 |   0 | 0.01 |   0 |   0 |
| 2005 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 | 0.2 |   0 | 0.02 |   0 | 0.01 |   0 |   0 |
| 2006 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 | 0.2 |   0 | 0.02 |   0 | 0.01 |   0 |   0 |
| 2007 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 | 0.2 |   0 | 0.02 |   0 | 0.01 |   0 |   0 |
| 2008 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 | 0.2 |   0 | 0.02 |   0 | 0.01 |   0 |   0 |
| 2009 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 | 0.2 |   0 | 0.02 |   0 | 0.01 |   0 |   0 |
| 2010 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 | 0.2 |   0 | 0.02 |   0 | 0.01 |   0 |   0 |
| 2011 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 | 0.2 |   0 | 0.02 |   0 | 0.01 |   0 |   0 |
| 2012 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 | 0.2 |   0 | 0.02 |   0 | 0.01 |   0 |   0 |
| 2013 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 | 0.2 |   0 | 0.02 |   0 | 0.01 |   0 |   0 |
| 2014 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 | 0.2 |   0 | 0.02 |   0 | 0.01 |   0 |   0 |
| 2015 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 | 0.2 |   0 | 0.02 |   0 | 0.01 |   0 |   0 |
| 2016 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 | 0.2 |   0 | 0.02 |   0 | 0.01 |   0 |   0 |
| 2017 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 | 0.2 |   0 | 0.02 |   0 | 0.01 |   0 |   0 |
| 2018 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 | 0.2 |   0 | 0.02 |   0 | 0.01 |   0 |   0 |
| 2019 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 | 0.2 |   0 | 0.02 |   0 | 0.01 |   0 |   0 |
| 2020 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 | 0.2 |   0 | 0.02 |   0 | 0.01 |   0 |   0 |
| 2021 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 | 0.2 |   0 | 0.02 |   0 | 0.01 |   0 |   0 |
| 2022 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 | 0.2 |   0 | 0.02 |   0 | 0.01 |   0 |   0 |
| 2023 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 | 0.2 |   0 | 0.02 |   0 | 0.01 |   0 |   0 |
| 2024 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 | 0.2 |   0 | 0.02 |   0 | 0.01 |   0 |   0 |
| 2025 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 | 0.2 |   0 | 0.02 |   0 | 0.01 |   0 |   0 |
| 2026 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 | 0.2 |   0 | 0.02 |   0 | 0.01 |   0 |   0 |
| 2027 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 | 0.2 |   0 | 0.02 |   0 | 0.01 |   0 |   0 |
| 2028 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 | 0.2 |   0 | 0.02 |   0 | 0.01 |   0 |   0 |
| 2029 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 | 0.2 |   0 | 0.02 |   0 | 0.01 |   0 |   0 |
| 2030 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 | 0.2 |   0 | 0.02 |   0 | 0.01 |   0 |   0 |
| 2031 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 | 0.2 |   0 | 0.02 |   0 | 0.01 |   0 |   0 |
| 2032 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 | 0.2 |   0 | 0.02 |   0 | 0.01 |   0 |   0 |
| 2033 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 | 0.2 |   0 | 0.02 |   0 | 0.01 |   0 |   0 |
| 2034 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 | 0.2 |   0 | 0.02 |   0 | 0.01 |   0 |   0 |
| 2035 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 | 0.2 |   0 | 0.02 |   0 | 0.01 |   0 |   0 |
| 2036 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 | 0.2 |   0 | 0.02 |   0 | 0.01 |   0 |   0 |
| 2037 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 | 0.2 |   0 | 0.02 |   0 | 0.01 |   0 |   0 |
| 2038 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 | 0.2 |   0 | 0.02 |   0 | 0.01 |   0 |   0 |
| 2039 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 | 0.2 |   0 | 0.02 |   0 | 0.01 |   0 |   0 |
| 2040 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 | 0.2 |   0 | 0.02 |   0 | 0.01 |   0 |   0 |
| 2041 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 | 0.2 |   0 | 0.02 |   0 | 0.01 |   0 |   0 |
| 2042 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 | 0.2 |   0 | 0.02 |   0 | 0.01 |   0 |   0 |
| 2043 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 | 0.2 |   0 | 0.02 |   0 | 0.01 |   0 |   0 |
| 2044 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 | 0.2 |   0 | 0.02 |   0 | 0.01 |   0 |   0 |
| 2045 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 | 0.2 |   0 | 0.02 |   0 | 0.01 |   0 |   0 |
| 2046 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 | 0.2 |   0 | 0.02 |   0 | 0.01 |   0 |   0 |
| 2047 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 | 0.2 |   0 | 0.02 |   0 | 0.01 |   0 |   0 |
| 2048 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 | 0.2 |   0 | 0.02 |   0 | 0.01 |   0 |   0 |
| 2049 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 | 0.2 |   0 | 0.02 |   0 | 0.01 |   0 |   0 |
| 2050 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 | 0.2 |   0 | 0.02 |   0 | 0.01 |   0 |   0 |



label: H=D-F
M=J*L
O=J*N
Q=J*P
I=B+D-F
J=C+E-G
R=M+Q+O
labeled_formulas: H=D-F
M=J*L
O=J*N
Q=J*P
I=B+D-F
J=C+E-G
R=M+Q+O
output: {"Arithmetic-Relationship": ["H=D-F", "M=J*L", "O=J*N", "Q=J*P", "I=B+D-F", "J=C+E-G", "R=M+Q+O"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_636355___xlsx_5638955a30dc0d4f86f9bb42b310d92f10609b91.xlsx___line_307