YES

TRS:

  half(0()) -> 0()
  half(s(s(x))) -> s(half(x))
  log(s(0())) -> 0()
  log(s(s(x))) -> s(log(s(half(x))))

linear polynomial interpretations on N:

  half_A(x1) = x1
  half#_A(x1) = x1
  0_A = 1
  0#_A = 1
  s_A(x1) = x1 + 2
  s#_A(x1) = x1 + 2
  log_A(x1) = x1 + 1
  log#_A(x1) = x1 + 1

precedence:

  half = s = log > 0