p1 Orientation of three rules is wrong. They should read f(x+y) → f(x) + f(y), g(x+y) → g(x) + g(y), and g(y) + f(x) → f(y) + g(x).

p3 Example 9: The same holds. Besides it,
f(x +_{a} y) + z and g(x +_{a} y) + z should read
f(x +_{a} y) +_{0} z and
g(x +_{a} y) +_{1} z, respectively.