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()))))))

linear polynomial interpretations on N:

  le_A(x1,x2) = x1
  le#_A(x1,x2) = 4
  0_A = 2
  0#_A = 2
  true_A = 1
  true#_A = 3
  s_A(x1) = x1 + 3
  s#_A(x1) = x1 + 1
  false_A = 1
  false#_A = 0
  minus_A(x1,x2) = x1
  minus#_A(x1,x2) = x1 + 2
  if_minus_A(x1,x2,x3) = x2
  if_minus#_A(x1,x2,x3) = x2 + 1
  quot_A(x1,x2) = x1
  quot#_A(x1,x2) = x1 + 1
  log_A(x1) = x1
  log#_A(x1) = x1 + 1

precedence:

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