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{8, 7 + x1}
  not#_A(x1) = max{2, 4}
  xor_A(x1,x2) = max{7, 3 + x1, 2 + x2}
  xor#_A(x1,x2) = max{3, 1, 4}
  true_A = 6
  true#_A = 3
  or_A(x1,x2) = max{3, 5 + x1, 9 + x2}
  or#_A(x1,x2) = max{6, 6 + x1, 6}
  and_A(x1,x2) = max{5, 1 + x1, 3}
  and#_A(x1,x2) = max{5, -2, 5}
  implies_A(x1,x2) = max{6, 10 + x1, 6}
  implies#_A(x1,x2) = max{2, 5, 2}
  false_A = 4
  false#_A = 0

precedence:

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