#-------------------------------------------------------------

# There exists a right-neutral element (0).
f(X,0)=X.

# For each X, there is a right inverse element i(X).
f(X,i(X))=0.

# f is associative.
f(f(X,Y),Z)=f(X,f(Y,Z)).

# The square of each element is the identity
f(X,X)=0.

# Hypothesis: f is commutative
f(a,b)!=f(b,a).