Given a system with multiple equations, where we know the values and the result, but not the operations between the values:
\begin{cases} 3 ⊕ 5 ⊙ 2 = 13 \\ 7 ⊕ 2 ⊙ 4 = 10 \\ 4 ⊕ 3 ⊙ 3 = 9 \end{cases}
Is there an algorithmic way to deduce $⊕$ and $⊙$ (which in this case would be multiplication and subtraction, respectively)? Like a system of equations where the unknowns are the operations themselves? Does this have a name? Are there ways of calculating it?