YES

TRS:

  implies(not(x),y) -> or(x,y)
  implies(not(x),or(y,z)) -> implies(y,or(x,z))
  implies(x,or(y,z)) -> or(y,implies(x,z))

linear polynomial interpretations on N:

  implies_A(x1,x2) = x1 + x2 + 1
  implies#_A(x1,x2) = x1 + x2
  not_A(x1) = x1 + 1
  not#_A(x1) = 0
  or_A(x1,x2) = x1 + x2 + 1
  or#_A(x1,x2) = 0

precedence:

  implies = not > or