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()))))))

linear polynomial interpretations on N:

  pred_A(x1) = x1
  pred#_A(x1) = 0
  s_A(x1) = x1 + 4
  s#_A(x1) = 7
  minus_A(x1,x2) = x1
  minus#_A(x1,x2) = x1 + 1
  0_A = 1
  0#_A = 6
  quot_A(x1,x2) = x1
  quot#_A(x1,x2) = x1 + 6
  log_A(x1) = x1
  log#_A(x1) = x1

precedence:

  log > s > 0 > quot > pred = minus