YES

(VAR x)
(RULES
  and(x,not(n1())) -> not(n1())
  or(x,not(n1())) -> x
  not(not(n1())) -> n1()
  n0() -> not(n1())
  or(x,n1()) -> n1()
  and(x,n1()) -> x
)

(COMMENT
Termination is shown by ELPO with interpretations on natural numbers

  and_A(x1,x2) = x1 + x2
  n0_A = 2
  n1_A = 1
  or_A(x1,x2) = x1 + 3
  not_A(x1) = x1 + 1
  and#_A(x1,x2) = x1 + x2
  n0#_A = 0
  n1#_A = 0
  or#_A(x1,x2) = x1 + x2
  not#_A(x1) = x1

and precedence:

and > or > n0 > n1 > not
)