YES

TRS:

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

max/plus interpretations on N:

  half_A(x1) = max{1, -7 + x1}
  half#_A(x1) = max{1, -1}
  0_A = 1
  0#_A = 3
  s_A(x1) = max{9, 7 + x1}
  s#_A(x1) = max{2, 3}
  log_A(x1) = max{3, 1 + x1}
  log#_A(x1) = max{0, -3 + x1}

precedence:

  s > log > half > 0