YES

TRS:

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

max/plus interpretations on N:

  not_A(x1) = max{0, x1}
  not#_A(x1) = max{0, x1}
  xor_A(x1,x2) = max{0, x1, x2}
  xor#_A(x1,x2) = max{0, x1, x2}
  true_A = 0
  true#_A = 0
  implies_A(x1,x2) = max{0, x1, x2}
  implies#_A(x1,x2) = max{0, x1, x2}
  and_A(x1,x2) = max{0, x1, x2}
  and#_A(x1,x2) = max{0, x1, x2}
  or_A(x1,x2) = max{0, x1, x2}
  or#_A(x1,x2) = max{0, x1, x2}
  =_A(x1,x2) = max{0, x1, x2}
  =#_A(x1,x2) = max{0, x1, x2}

precedence:

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