YES

TRS:

  le(0(),y) -> true()
  le(s(x),0()) -> false()
  le(s(x),s(y)) -> le(x,y)
  minus(0(),y) -> 0()
  minus(s(x),y) -> if_minus(le(s(x),y),s(x),y)
  if_minus(true(),s(x),y) -> 0()
  if_minus(false(),s(x),y) -> s(minus(x,y))
  quot(0(),s(y)) -> 0()
  quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
  log(s(0())) -> 0()
  log(s(s(x))) -> s(log(s(quot(x,s(s(0()))))))

max/plus interpretations on N:

  le_A(x1,x2) = max{1, -1, 14}
  le#_A(x1,x2) = max{16, 1, 2}
  0_A = 9
  0#_A = 8
  true_A = 2
  true#_A = 0
  s_A(x1) = max{17, 34 + x1}
  s#_A(x1) = max{14, 17}
  false_A = 14
  false#_A = 17
  minus_A(x1,x2) = max{0, x1, -1}
  minus#_A(x1,x2) = max{3, -2 + x1, 18}
  if_minus_A(x1,x2,x3) = max{18, -1, x2, 0}
  if_minus#_A(x1,x2,x3) = max{2, 5 + x1, -15 + x2, 7}
  quot_A(x1,x2) = max{0, x1, -15}
  quot#_A(x1,x2) = max{7, x1, 9}
  log_A(x1) = max{1, -18 + x1}
  log#_A(x1) = max{13, -7 + x1}

precedence:

  log > quot > minus > le = if_minus > true = s > 0 > false