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.