YES

TRS:

  and(x,false()) -> false()
  and(x,not(false())) -> x
  not(not(x)) -> x
  implies(false(),y) -> not(false())
  implies(x,false()) -> not(x)
  implies(not(x),not(y)) -> implies(y,and(x,y))

max/plus interpretations on N:

  and_A(x1,x2) = max{1, 4 + x1, 1 + x2}
  and#_A(x1,x2) = max{1, 4 + x1, 1 + x2}
  false_A = 0
  false#_A = 0
  not_A(x1) = max{3, 3 + x1}
  not#_A(x1) = max{3, 3 + x1}
  implies_A(x1,x2) = max{4, 4 + x1, 2 + x2}
  implies#_A(x1,x2) = max{4, 4 + x1, 2 + x2}

precedence:

  false > implies > and = not