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()))

linear polynomial interpretations on N:

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

precedence:

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