YES

TRS:

  pred(s(x)) -> x
  minus(x,0()) -> x
  minus(x,s(y)) -> pred(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:

  pred_A(x1) = max{1, x1}
  pred#_A(x1) = max{15, 15}
  s_A(x1) = max{18, 7 + x1}
  s#_A(x1) = max{2, 1}
  minus_A(x1,x2) = max{1, x1, 0}
  minus#_A(x1,x2) = max{15, 15, 15}
  0_A = 6
  0#_A = 0
  quot_A(x1,x2) = max{5, x1, -2}
  quot#_A(x1,x2) = max{18, 12 + x1, 16}
  log_A(x1) = max{5, 3 + x1}
  log#_A(x1) = max{3, -1 + x1}

precedence:

  log > s > 0 > quot > minus > pred