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) = 2
  half#_A(x1) = 0
  0_A = 1
  0#_A = 2
  s_A(x1) = 1
  s#_A(x1) = 1
  log_A(x1) = 2
  log#_A(x1) = 3

precedence:

  log > 0 > s > half