YES

TRS:

  not(x) -> xor(x,true())
  or(x,y) -> xor(and(x,y),xor(x,y))
  implies(x,y) -> xor(and(x,y),xor(x,true()))
  and(x,true()) -> x
  and(x,false()) -> false()
  and(x,x) -> x
  xor(x,false()) -> x
  xor(x,x) -> false()
  and(xor(x,y),z) -> xor(and(x,z),and(y,z))

max/plus interpretations on N:

  not_A(x1) = max{4, 1 + x1}
  not#_A(x1) = max{4, 1 + x1}
  xor_A(x1,x2) = max{4, x1, x2}
  xor#_A(x1,x2) = max{4, x1, x2}
  true_A = 4
  true#_A = 4
  or_A(x1,x2) = max{4, 3 + x1, 3 + x2}
  or#_A(x1,x2) = max{4, 3 + x1, 3 + x2}
  and_A(x1,x2) = max{4, 2 + x1, 1 + x2}
  and#_A(x1,x2) = max{4, 2 + x1, 1 + x2}
  implies_A(x1,x2) = max{3, 3 + x1, 4 + x2}
  implies#_A(x1,x2) = max{3, 3 + x1, 4 + x2}
  false_A = 1
  false#_A = 1

precedence:

  or = implies = false > not = and > xor = true