MAYBE
Time: 0.007377
TRS:
 {       D t() -> 1(),
  D constant() -> 0(),
     D +(x, y) -> +(D x, D y),
     D *(x, y) -> +(*(y, D x), *(x, D y)),
     D -(x, y) -> -(D x, D y),
     D minus x -> minus D x,
   D div(x, y) -> -(div(D x, y), div(*(x, D y), pow(y, 2()))),
   D pow(x, y) -> +(*(*(y, pow(x, -(y, 1()))), D x), *(*(pow(x, y), ln x), D y)),
        D ln x -> div(D x, x)}
 DP:
  DP:
   {  D# +(x, y) -> D# x,
      D# +(x, y) -> D# y,
      D# *(x, y) -> D# x,
      D# *(x, y) -> D# y,
      D# -(x, y) -> D# x,
      D# -(x, y) -> D# y,
      D# minus x -> D# x,
    D# div(x, y) -> D# x,
    D# div(x, y) -> D# y,
    D# pow(x, y) -> D# x,
    D# pow(x, y) -> D# y,
         D# ln x -> D# x}
  TRS:
  {       D t() -> 1(),
   D constant() -> 0(),
      D +(x, y) -> +(D x, D y),
      D *(x, y) -> +(*(y, D x), *(x, D y)),
      D -(x, y) -> -(D x, D y),
      D minus x -> minus D x,
    D div(x, y) -> -(div(D x, y), div(*(x, D y), pow(y, 2()))),
    D pow(x, y) -> +(*(*(y, pow(x, -(y, 1()))), D x), *(*(pow(x, y), ln x), D y)),
         D ln x -> div(D x, x)}
  UR:
   {}
   EDG:
    {(D# *(x, y) -> D# y, D# ln x -> D# x)
     (D# *(x, y) -> D# y, D# pow(x, y) -> D# y)
     (D# *(x, y) -> D# y, D# pow(x, y) -> D# x)
     (D# *(x, y) -> D# y, D# div(x, y) -> D# y)
     (D# *(x, y) -> D# y, D# div(x, y) -> D# x)
     (D# *(x, y) -> D# y, D# minus x -> D# x)
     (D# *(x, y) -> D# y, D# -(x, y) -> D# y)
     (D# *(x, y) -> D# y, D# -(x, y) -> D# x)
     (D# *(x, y) -> D# y, D# *(x, y) -> D# y)
     (D# *(x, y) -> D# y, D# *(x, y) -> D# x)
     (D# *(x, y) -> D# y, D# +(x, y) -> D# y)
     (D# *(x, y) -> D# y, D# +(x, y) -> D# x)
     (D# div(x, y) -> D# y, D# ln x -> D# x)
     (D# div(x, y) -> D# y, D# pow(x, y) -> D# y)
     (D# div(x, y) -> D# y, D# pow(x, y) -> D# x)
     (D# div(x, y) -> D# y, D# div(x, y) -> D# y)
     (D# div(x, y) -> D# y, D# div(x, y) -> D# x)
     (D# div(x, y) -> D# y, D# minus x -> D# x)
     (D# div(x, y) -> D# y, D# -(x, y) -> D# y)
     (D# div(x, y) -> D# y, D# -(x, y) -> D# x)
     (D# div(x, y) -> D# y, D# *(x, y) -> D# y)
     (D# div(x, y) -> D# y, D# *(x, y) -> D# x)
     (D# div(x, y) -> D# y, D# +(x, y) -> D# y)
     (D# div(x, y) -> D# y, D# +(x, y) -> D# x)
     (D# +(x, y) -> D# x, D# ln x -> D# x)
     (D# +(x, y) -> D# x, D# pow(x, y) -> D# y)
     (D# +(x, y) -> D# x, D# pow(x, y) -> D# x)
     (D# +(x, y) -> D# x, D# div(x, y) -> D# y)
     (D# +(x, y) -> D# x, D# div(x, y) -> D# x)
     (D# +(x, y) -> D# x, D# minus x -> D# x)
     (D# +(x, y) -> D# x, D# -(x, y) -> D# y)
     (D# +(x, y) -> D# x, D# -(x, y) -> D# x)
     (D# +(x, y) -> D# x, D# *(x, y) -> D# y)
     (D# +(x, y) -> D# x, D# *(x, y) -> D# x)
     (D# +(x, y) -> D# x, D# +(x, y) -> D# y)
     (D# +(x, y) -> D# x, D# +(x, y) -> D# x)
     (D# -(x, y) -> D# x, D# ln x -> D# x)
     (D# -(x, y) -> D# x, D# pow(x, y) -> D# y)
     (D# -(x, y) -> D# x, D# pow(x, y) -> D# x)
     (D# -(x, y) -> D# x, D# div(x, y) -> D# y)
     (D# -(x, y) -> D# x, D# div(x, y) -> D# x)
     (D# -(x, y) -> D# x, D# minus x -> D# x)
     (D# -(x, y) -> D# x, D# -(x, y) -> D# y)
     (D# -(x, y) -> D# x, D# -(x, y) -> D# x)
     (D# -(x, y) -> D# x, D# *(x, y) -> D# y)
     (D# -(x, y) -> D# x, D# *(x, y) -> D# x)
     (D# -(x, y) -> D# x, D# +(x, y) -> D# y)
     (D# -(x, y) -> D# x, D# +(x, y) -> D# x)
     (D# div(x, y) -> D# x, D# ln x -> D# x)
     (D# div(x, y) -> D# x, D# pow(x, y) -> D# y)
     (D# div(x, y) -> D# x, D# pow(x, y) -> D# x)
     (D# div(x, y) -> D# x, D# div(x, y) -> D# y)
     (D# div(x, y) -> D# x, D# div(x, y) -> D# x)
     (D# div(x, y) -> D# x, D# minus x -> D# x)
     (D# div(x, y) -> D# x, D# -(x, y) -> D# y)
     (D# div(x, y) -> D# x, D# -(x, y) -> D# x)
     (D# div(x, y) -> D# x, D# *(x, y) -> D# y)
     (D# div(x, y) -> D# x, D# *(x, y) -> D# x)
     (D# div(x, y) -> D# x, D# +(x, y) -> D# y)
     (D# div(x, y) -> D# x, D# +(x, y) -> D# x)
     (D# ln x -> D# x, D# ln x -> D# x)
     (D# ln x -> D# x, D# pow(x, y) -> D# y)
     (D# ln x -> D# x, D# pow(x, y) -> D# x)
     (D# ln x -> D# x, D# div(x, y) -> D# y)
     (D# ln x -> D# x, D# div(x, y) -> D# x)
     (D# ln x -> D# x, D# minus x -> D# x)
     (D# ln x -> D# x, D# -(x, y) -> D# y)
     (D# ln x -> D# x, D# -(x, y) -> D# x)
     (D# ln x -> D# x, D# *(x, y) -> D# y)
     (D# ln x -> D# x, D# *(x, y) -> D# x)
     (D# ln x -> D# x, D# +(x, y) -> D# y)
     (D# ln x -> D# x, D# +(x, y) -> D# x)
     (D# pow(x, y) -> D# x, D# +(x, y) -> D# x)
     (D# pow(x, y) -> D# x, D# +(x, y) -> D# y)
     (D# pow(x, y) -> D# x, D# *(x, y) -> D# x)
     (D# pow(x, y) -> D# x, D# *(x, y) -> D# y)
     (D# pow(x, y) -> D# x, D# -(x, y) -> D# x)
     (D# pow(x, y) -> D# x, D# -(x, y) -> D# y)
     (D# pow(x, y) -> D# x, D# minus x -> D# x)
     (D# pow(x, y) -> D# x, D# div(x, y) -> D# x)
     (D# pow(x, y) -> D# x, D# div(x, y) -> D# y)
     (D# pow(x, y) -> D# x, D# pow(x, y) -> D# x)
     (D# pow(x, y) -> D# x, D# pow(x, y) -> D# y)
     (D# pow(x, y) -> D# x, D# ln x -> D# x)
     (D# minus x -> D# x, D# +(x, y) -> D# x)
     (D# minus x -> D# x, D# +(x, y) -> D# y)
     (D# minus x -> D# x, D# *(x, y) -> D# x)
     (D# minus x -> D# x, D# *(x, y) -> D# y)
     (D# minus x -> D# x, D# -(x, y) -> D# x)
     (D# minus x -> D# x, D# -(x, y) -> D# y)
     (D# minus x -> D# x, D# minus x -> D# x)
     (D# minus x -> D# x, D# div(x, y) -> D# x)
     (D# minus x -> D# x, D# div(x, y) -> D# y)
     (D# minus x -> D# x, D# pow(x, y) -> D# x)
     (D# minus x -> D# x, D# pow(x, y) -> D# y)
     (D# minus x -> D# x, D# ln x -> D# x)
     (D# *(x, y) -> D# x, D# +(x, y) -> D# x)
     (D# *(x, y) -> D# x, D# +(x, y) -> D# y)
     (D# *(x, y) -> D# x, D# *(x, y) -> D# x)
     (D# *(x, y) -> D# x, D# *(x, y) -> D# y)
     (D# *(x, y) -> D# x, D# -(x, y) -> D# x)
     (D# *(x, y) -> D# x, D# -(x, y) -> D# y)
     (D# *(x, y) -> D# x, D# minus x -> D# x)
     (D# *(x, y) -> D# x, D# div(x, y) -> D# x)
     (D# *(x, y) -> D# x, D# div(x, y) -> D# y)
     (D# *(x, y) -> D# x, D# pow(x, y) -> D# x)
     (D# *(x, y) -> D# x, D# pow(x, y) -> D# y)
     (D# *(x, y) -> D# x, D# ln x -> D# x)
     (D# pow(x, y) -> D# y, D# +(x, y) -> D# x)
     (D# pow(x, y) -> D# y, D# +(x, y) -> D# y)
     (D# pow(x, y) -> D# y, D# *(x, y) -> D# x)
     (D# pow(x, y) -> D# y, D# *(x, y) -> D# y)
     (D# pow(x, y) -> D# y, D# -(x, y) -> D# x)
     (D# pow(x, y) -> D# y, D# -(x, y) -> D# y)
     (D# pow(x, y) -> D# y, D# minus x -> D# x)
     (D# pow(x, y) -> D# y, D# div(x, y) -> D# x)
     (D# pow(x, y) -> D# y, D# div(x, y) -> D# y)
     (D# pow(x, y) -> D# y, D# pow(x, y) -> D# x)
     (D# pow(x, y) -> D# y, D# pow(x, y) -> D# y)
     (D# pow(x, y) -> D# y, D# ln x -> D# x)
     (D# -(x, y) -> D# y, D# +(x, y) -> D# x)
     (D# -(x, y) -> D# y, D# +(x, y) -> D# y)
     (D# -(x, y) -> D# y, D# *(x, y) -> D# x)
     (D# -(x, y) -> D# y, D# *(x, y) -> D# y)
     (D# -(x, y) -> D# y, D# -(x, y) -> D# x)
     (D# -(x, y) -> D# y, D# -(x, y) -> D# y)
     (D# -(x, y) -> D# y, D# minus x -> D# x)
     (D# -(x, y) -> D# y, D# div(x, y) -> D# x)
     (D# -(x, y) -> D# y, D# div(x, y) -> D# y)
     (D# -(x, y) -> D# y, D# pow(x, y) -> D# x)
     (D# -(x, y) -> D# y, D# pow(x, y) -> D# y)
     (D# -(x, y) -> D# y, D# ln x -> D# x)
     (D# +(x, y) -> D# y, D# +(x, y) -> D# x)
     (D# +(x, y) -> D# y, D# +(x, y) -> D# y)
     (D# +(x, y) -> D# y, D# *(x, y) -> D# x)
     (D# +(x, y) -> D# y, D# *(x, y) -> D# y)
     (D# +(x, y) -> D# y, D# -(x, y) -> D# x)
     (D# +(x, y) -> D# y, D# -(x, y) -> D# y)
     (D# +(x, y) -> D# y, D# minus x -> D# x)
     (D# +(x, y) -> D# y, D# div(x, y) -> D# x)
     (D# +(x, y) -> D# y, D# div(x, y) -> D# y)
     (D# +(x, y) -> D# y, D# pow(x, y) -> D# x)
     (D# +(x, y) -> D# y, D# pow(x, y) -> D# y)
     (D# +(x, y) -> D# y, D# ln x -> D# x)}
    STATUS:
     arrows: 0.000000
     SCCS (1):
      Scc:
       {  D# +(x, y) -> D# x,
          D# +(x, y) -> D# y,
          D# *(x, y) -> D# x,
          D# *(x, y) -> D# y,
          D# -(x, y) -> D# x,
          D# -(x, y) -> D# y,
          D# minus x -> D# x,
        D# div(x, y) -> D# x,
        D# div(x, y) -> D# y,
        D# pow(x, y) -> D# x,
        D# pow(x, y) -> D# y,
             D# ln x -> D# x}
      
      SCC (12):
       Strict:
        {  D# +(x, y) -> D# x,
           D# +(x, y) -> D# y,
           D# *(x, y) -> D# x,
           D# *(x, y) -> D# y,
           D# -(x, y) -> D# x,
           D# -(x, y) -> D# y,
           D# minus x -> D# x,
         D# div(x, y) -> D# x,
         D# div(x, y) -> D# y,
         D# pow(x, y) -> D# x,
         D# pow(x, y) -> D# y,
              D# ln x -> D# x}
       Weak:
       {       D t() -> 1(),
        D constant() -> 0(),
           D +(x, y) -> +(D x, D y),
           D *(x, y) -> +(*(y, D x), *(x, D y)),
           D -(x, y) -> -(D x, D y),
           D minus x -> minus D x,
         D div(x, y) -> -(div(D x, y), div(*(x, D y), pow(y, 2()))),
         D pow(x, y) -> +(*(*(y, pow(x, -(y, 1()))), D x), *(*(pow(x, y), ln x), D y)),
              D ln x -> div(D x, x)}
       Open