Left-right fold equivalence

For finite lists, if $x\oplus (y\otimes z)=(x\oplus y)\otimes z$ and $x\oplus a=a\otimes x$, then the right fold with step $\oplus$ and seed $a$ equals the left fold with step $\otimes$ and seed $a$. The two steps need not be identical. Equality of the resulting values does not imply equal time complexity; list concatenation is an important example.