MAYBE
Time: 0.000780
TRS:
 {       purge nil() -> nil(),
       purge .(x, y) -> .(x, purge remove(x, y)),
    remove(x, nil()) -> nil(),
  remove(x, .(y, z)) -> if(=(x, y), remove(x, z), .(y, remove(x, z)))}
 DP:
  DP:
   {     purge# .(x, y) -> purge# remove(x, y),
         purge# .(x, y) -> remove#(x, y),
    remove#(x, .(y, z)) -> remove#(x, z)}
  TRS:
  {       purge nil() -> nil(),
        purge .(x, y) -> .(x, purge remove(x, y)),
     remove(x, nil()) -> nil(),
   remove(x, .(y, z)) -> if(=(x, y), remove(x, z), .(y, remove(x, z)))}
  UR:
   {  remove(x, nil()) -> nil(),
    remove(x, .(y, z)) -> if(=(x, y), remove(x, z), .(y, remove(x, z))),
               a(w, v) -> w,
               a(w, v) -> v}
   EDG:
    {(remove#(x, .(y, z)) -> remove#(x, z), remove#(x, .(y, z)) -> remove#(x, z))
     (purge# .(x, y) -> remove#(x, y), remove#(x, .(y, z)) -> remove#(x, z))
     (purge# .(x, y) -> purge# remove(x, y), purge# .(x, y) -> purge# remove(x, y))
     (purge# .(x, y) -> purge# remove(x, y), purge# .(x, y) -> remove#(x, y))}
    STATUS:
     arrows: 0.555556
     SCCS (2):
      Scc:
       {purge# .(x, y) -> purge# remove(x, y)}
      Scc:
       {remove#(x, .(y, z)) -> remove#(x, z)}
      
      SCC (1):
       Strict:
        {purge# .(x, y) -> purge# remove(x, y)}
       Weak:
       {       purge nil() -> nil(),
             purge .(x, y) -> .(x, purge remove(x, y)),
          remove(x, nil()) -> nil(),
        remove(x, .(y, z)) -> if(=(x, y), remove(x, z), .(y, remove(x, z)))}
       Open
      
      SCC (1):
       Strict:
        {remove#(x, .(y, z)) -> remove#(x, z)}
       Weak:
       {       purge nil() -> nil(),
             purge .(x, y) -> .(x, purge remove(x, y)),
          remove(x, nil()) -> nil(),
        remove(x, .(y, z)) -> if(=(x, y), remove(x, z), .(y, remove(x, z)))}
       Open