TRS: { not(x) -> xor(x, true()), implies(x, y) -> xor(and(x, y), xor(x, true())), or(x, y) -> xor(and(x, y), xor(x, y)), =(x, y) -> xor(x, xor(y, true()))} POP*: Quasi-Precedence: or > xor, or > and, not > true, not > xor, implies > and, implies > true, implies > xor, = > true, = > xor empty Normal: pi(=) = [1,2], pi(or) = [1,2], pi(implies) = [1,2], pi(not) = [1] Safe: pi(and) = [1,2], pi(xor) = [1,2] Predicative System: { not(x;) -> xor(;x,true()), implies(x,y;) -> xor(;and(;x,y),xor(;x,true())), or(x,y;) -> xor(;and(;x,y),xor(;x,y)), =(x,y;) -> xor(;x,xor(;y,true()))} Qed