YES

TRS:

  min(X,0()) -> X
  min(s(X),s(Y)) -> min(X,Y)
  quot(0(),s(Y)) -> 0()
  quot(s(X),s(Y)) -> s(quot(min(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:

  min_A(x1,x2) = x1
  min#_A(x1,x2) = 0
  0_A = 1
  0#_A = 6
  s_A(x1) = x1 + 4
  s#_A(x1) = 7
  quot_A(x1,x2) = x1
  quot#_A(x1,x2) = x1 + 6
  log_A(x1) = x1
  log#_A(x1) = x1

precedence:

  log > quot > min = s > 0