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))

linear polynomial interpretations on N:

  not_A(x1) = x1 + 1
  not#_A(x1) = x1 + 2
  xor_A(x1,x2) = x1 + 1
  xor#_A(x1,x2) = 1
  true_A = 1
  true#_A = 0
  or_A(x1,x2) = x1 + x2 + 2
  or#_A(x1,x2) = x1 + x2 + 3
  and_A(x1,x2) = x1 + x2 + 1
  and#_A(x1,x2) = x2 + 2
  implies_A(x1,x2) = x1 + x2 + 2
  implies#_A(x1,x2) = x1 + x2 + 3
  false_A = 1
  false#_A = 0

precedence:

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