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

precedence:

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