MAYBE

Problem:
 active(f(a(),X,X)) -> mark(f(X,b(),b()))
 active(b()) -> mark(a())
 mark(f(X1,X2,X3)) -> active(f(X1,mark(X2),X3))
 mark(a()) -> active(a())
 mark(b()) -> active(b())
 f(mark(X1),X2,X3) -> f(X1,X2,X3)
 f(X1,mark(X2),X3) -> f(X1,X2,X3)
 f(X1,X2,mark(X3)) -> f(X1,X2,X3)
 f(active(X1),X2,X3) -> f(X1,X2,X3)
 f(X1,active(X2),X3) -> f(X1,X2,X3)
 f(X1,X2,active(X3)) -> f(X1,X2,X3)

Proof:
 DP Processor:
  DPs:
   active#(f(a(),X,X)) -> f#(X,b(),b())
   active#(f(a(),X,X)) -> mark#(f(X,b(),b()))
   active#(b()) -> mark#(a())
   mark#(f(X1,X2,X3)) -> mark#(X2)
   mark#(f(X1,X2,X3)) -> f#(X1,mark(X2),X3)
   mark#(f(X1,X2,X3)) -> active#(f(X1,mark(X2),X3))
   mark#(a()) -> active#(a())
   mark#(b()) -> active#(b())
   f#(mark(X1),X2,X3) -> f#(X1,X2,X3)
   f#(X1,mark(X2),X3) -> f#(X1,X2,X3)
   f#(X1,X2,mark(X3)) -> f#(X1,X2,X3)
   f#(active(X1),X2,X3) -> f#(X1,X2,X3)
   f#(X1,active(X2),X3) -> f#(X1,X2,X3)
   f#(X1,X2,active(X3)) -> f#(X1,X2,X3)
  TRS:
   active(f(a(),X,X)) -> mark(f(X,b(),b()))
   active(b()) -> mark(a())
   mark(f(X1,X2,X3)) -> active(f(X1,mark(X2),X3))
   mark(a()) -> active(a())
   mark(b()) -> active(b())
   f(mark(X1),X2,X3) -> f(X1,X2,X3)
   f(X1,mark(X2),X3) -> f(X1,X2,X3)
   f(X1,X2,mark(X3)) -> f(X1,X2,X3)
   f(active(X1),X2,X3) -> f(X1,X2,X3)
   f(X1,active(X2),X3) -> f(X1,X2,X3)
   f(X1,X2,active(X3)) -> f(X1,X2,X3)
  EDG Processor:
   DPs:
    active#(f(a(),X,X)) -> f#(X,b(),b())
    active#(f(a(),X,X)) -> mark#(f(X,b(),b()))
    active#(b()) -> mark#(a())
    mark#(f(X1,X2,X3)) -> mark#(X2)
    mark#(f(X1,X2,X3)) -> f#(X1,mark(X2),X3)
    mark#(f(X1,X2,X3)) -> active#(f(X1,mark(X2),X3))
    mark#(a()) -> active#(a())
    mark#(b()) -> active#(b())
    f#(mark(X1),X2,X3) -> f#(X1,X2,X3)
    f#(X1,mark(X2),X3) -> f#(X1,X2,X3)
    f#(X1,X2,mark(X3)) -> f#(X1,X2,X3)
    f#(active(X1),X2,X3) -> f#(X1,X2,X3)
    f#(X1,active(X2),X3) -> f#(X1,X2,X3)
    f#(X1,X2,active(X3)) -> f#(X1,X2,X3)
   TRS:
    active(f(a(),X,X)) -> mark(f(X,b(),b()))
    active(b()) -> mark(a())
    mark(f(X1,X2,X3)) -> active(f(X1,mark(X2),X3))
    mark(a()) -> active(a())
    mark(b()) -> active(b())
    f(mark(X1),X2,X3) -> f(X1,X2,X3)
    f(X1,mark(X2),X3) -> f(X1,X2,X3)
    f(X1,X2,mark(X3)) -> f(X1,X2,X3)
    f(active(X1),X2,X3) -> f(X1,X2,X3)
    f(X1,active(X2),X3) -> f(X1,X2,X3)
    f(X1,X2,active(X3)) -> f(X1,X2,X3)
   graph:
    mark#(b()) -> active#(b()) -> active#(b()) -> mark#(a())
    mark#(f(X1,X2,X3)) -> mark#(X2) ->
    mark#(f(X1,X2,X3)) -> mark#(X2)
    mark#(f(X1,X2,X3)) -> mark#(X2) ->
    mark#(f(X1,X2,X3)) -> f#(X1,mark(X2),X3)
    mark#(f(X1,X2,X3)) -> mark#(X2) ->
    mark#(f(X1,X2,X3)) -> active#(f(X1,mark(X2),X3))
    mark#(f(X1,X2,X3)) -> mark#(X2) -> mark#(a()) -> active#(a())
    mark#(f(X1,X2,X3)) -> mark#(X2) ->
    mark#(b()) -> active#(b())
    mark#(f(X1,X2,X3)) -> f#(X1,mark(X2),X3) ->
    f#(mark(X1),X2,X3) -> f#(X1,X2,X3)
    mark#(f(X1,X2,X3)) -> f#(X1,mark(X2),X3) ->
    f#(X1,mark(X2),X3) -> f#(X1,X2,X3)
    mark#(f(X1,X2,X3)) -> f#(X1,mark(X2),X3) ->
    f#(X1,X2,mark(X3)) -> f#(X1,X2,X3)
    mark#(f(X1,X2,X3)) -> f#(X1,mark(X2),X3) ->
    f#(active(X1),X2,X3) -> f#(X1,X2,X3)
    mark#(f(X1,X2,X3)) -> f#(X1,mark(X2),X3) ->
    f#(X1,active(X2),X3) -> f#(X1,X2,X3)
    mark#(f(X1,X2,X3)) -> f#(X1,mark(X2),X3) ->
    f#(X1,X2,active(X3)) -> f#(X1,X2,X3)
    mark#(f(X1,X2,X3)) -> active#(f(X1,mark(X2),X3)) ->
    active#(f(a(),X,X)) -> f#(X,b(),b())
    mark#(f(X1,X2,X3)) -> active#(f(X1,mark(X2),X3)) ->
    active#(f(a(),X,X)) -> mark#(f(X,b(),b()))
    f#(mark(X1),X2,X3) -> f#(X1,X2,X3) ->
    f#(mark(X1),X2,X3) -> f#(X1,X2,X3)
    f#(mark(X1),X2,X3) -> f#(X1,X2,X3) ->
    f#(X1,mark(X2),X3) -> f#(X1,X2,X3)
    f#(mark(X1),X2,X3) -> f#(X1,X2,X3) ->
    f#(X1,X2,mark(X3)) -> f#(X1,X2,X3)
    f#(mark(X1),X2,X3) -> f#(X1,X2,X3) ->
    f#(active(X1),X2,X3) -> f#(X1,X2,X3)
    f#(mark(X1),X2,X3) -> f#(X1,X2,X3) ->
    f#(X1,active(X2),X3) -> f#(X1,X2,X3)
    f#(mark(X1),X2,X3) -> f#(X1,X2,X3) ->
    f#(X1,X2,active(X3)) -> f#(X1,X2,X3)
    f#(active(X1),X2,X3) -> f#(X1,X2,X3) ->
    f#(mark(X1),X2,X3) -> f#(X1,X2,X3)
    f#(active(X1),X2,X3) -> f#(X1,X2,X3) ->
    f#(X1,mark(X2),X3) -> f#(X1,X2,X3)
    f#(active(X1),X2,X3) -> f#(X1,X2,X3) ->
    f#(X1,X2,mark(X3)) -> f#(X1,X2,X3)
    f#(active(X1),X2,X3) -> f#(X1,X2,X3) ->
    f#(active(X1),X2,X3) -> f#(X1,X2,X3)
    f#(active(X1),X2,X3) -> f#(X1,X2,X3) ->
    f#(X1,active(X2),X3) -> f#(X1,X2,X3)
    f#(active(X1),X2,X3) -> f#(X1,X2,X3) ->
    f#(X1,X2,active(X3)) -> f#(X1,X2,X3)
    f#(X1,mark(X2),X3) -> f#(X1,X2,X3) ->
    f#(mark(X1),X2,X3) -> f#(X1,X2,X3)
    f#(X1,mark(X2),X3) -> f#(X1,X2,X3) ->
    f#(X1,mark(X2),X3) -> f#(X1,X2,X3)
    f#(X1,mark(X2),X3) -> f#(X1,X2,X3) ->
    f#(X1,X2,mark(X3)) -> f#(X1,X2,X3)
    f#(X1,mark(X2),X3) -> f#(X1,X2,X3) ->
    f#(active(X1),X2,X3) -> f#(X1,X2,X3)
    f#(X1,mark(X2),X3) -> f#(X1,X2,X3) ->
    f#(X1,active(X2),X3) -> f#(X1,X2,X3)
    f#(X1,mark(X2),X3) -> f#(X1,X2,X3) ->
    f#(X1,X2,active(X3)) -> f#(X1,X2,X3)
    f#(X1,active(X2),X3) -> f#(X1,X2,X3) ->
    f#(mark(X1),X2,X3) -> f#(X1,X2,X3)
    f#(X1,active(X2),X3) -> f#(X1,X2,X3) ->
    f#(X1,mark(X2),X3) -> f#(X1,X2,X3)
    f#(X1,active(X2),X3) -> f#(X1,X2,X3) ->
    f#(X1,X2,mark(X3)) -> f#(X1,X2,X3)
    f#(X1,active(X2),X3) -> f#(X1,X2,X3) ->
    f#(active(X1),X2,X3) -> f#(X1,X2,X3)
    f#(X1,active(X2),X3) -> f#(X1,X2,X3) ->
    f#(X1,active(X2),X3) -> f#(X1,X2,X3)
    f#(X1,active(X2),X3) -> f#(X1,X2,X3) ->
    f#(X1,X2,active(X3)) -> f#(X1,X2,X3)
    f#(X1,X2,mark(X3)) -> f#(X1,X2,X3) ->
    f#(mark(X1),X2,X3) -> f#(X1,X2,X3)
    f#(X1,X2,mark(X3)) -> f#(X1,X2,X3) ->
    f#(X1,mark(X2),X3) -> f#(X1,X2,X3)
    f#(X1,X2,mark(X3)) -> f#(X1,X2,X3) ->
    f#(X1,X2,mark(X3)) -> f#(X1,X2,X3)
    f#(X1,X2,mark(X3)) -> f#(X1,X2,X3) ->
    f#(active(X1),X2,X3) -> f#(X1,X2,X3)
    f#(X1,X2,mark(X3)) -> f#(X1,X2,X3) ->
    f#(X1,active(X2),X3) -> f#(X1,X2,X3)
    f#(X1,X2,mark(X3)) -> f#(X1,X2,X3) ->
    f#(X1,X2,active(X3)) -> f#(X1,X2,X3)
    f#(X1,X2,active(X3)) -> f#(X1,X2,X3) ->
    f#(mark(X1),X2,X3) -> f#(X1,X2,X3)
    f#(X1,X2,active(X3)) -> f#(X1,X2,X3) ->
    f#(X1,mark(X2),X3) -> f#(X1,X2,X3)
    f#(X1,X2,active(X3)) -> f#(X1,X2,X3) ->
    f#(X1,X2,mark(X3)) -> f#(X1,X2,X3)
    f#(X1,X2,active(X3)) -> f#(X1,X2,X3) ->
    f#(active(X1),X2,X3) -> f#(X1,X2,X3)
    f#(X1,X2,active(X3)) -> f#(X1,X2,X3) ->
    f#(X1,active(X2),X3) -> f#(X1,X2,X3)
    f#(X1,X2,active(X3)) -> f#(X1,X2,X3) ->
    f#(X1,X2,active(X3)) -> f#(X1,X2,X3)
    active#(b()) -> mark#(a()) ->
    mark#(a()) -> active#(a())
    active#(f(a(),X,X)) -> mark#(f(X,b(),b())) ->
    mark#(f(X1,X2,X3)) -> mark#(X2)
    active#(f(a(),X,X)) -> mark#(f(X,b(),b())) ->
    mark#(f(X1,X2,X3)) -> f#(X1,mark(X2),X3)
    active#(f(a(),X,X)) -> mark#(f(X,b(),b())) ->
    mark#(f(X1,X2,X3)) -> active#(f(X1,mark(X2),X3))
    active#(f(a(),X,X)) -> f#(X,b(),b()) ->
    f#(mark(X1),X2,X3) -> f#(X1,X2,X3)
    active#(f(a(),X,X)) -> f#(X,b(),b()) -> f#(active(X1),X2,X3) -> f#(X1,X2,X3)
   Restore Modifier:
    DPs:
     active#(f(a(),X,X)) -> f#(X,b(),b())
     active#(f(a(),X,X)) -> mark#(f(X,b(),b()))
     active#(b()) -> mark#(a())
     mark#(f(X1,X2,X3)) -> mark#(X2)
     mark#(f(X1,X2,X3)) -> f#(X1,mark(X2),X3)
     mark#(f(X1,X2,X3)) -> active#(f(X1,mark(X2),X3))
     mark#(a()) -> active#(a())
     mark#(b()) -> active#(b())
     f#(mark(X1),X2,X3) -> f#(X1,X2,X3)
     f#(X1,mark(X2),X3) -> f#(X1,X2,X3)
     f#(X1,X2,mark(X3)) -> f#(X1,X2,X3)
     f#(active(X1),X2,X3) -> f#(X1,X2,X3)
     f#(X1,active(X2),X3) -> f#(X1,X2,X3)
     f#(X1,X2,active(X3)) -> f#(X1,X2,X3)
    TRS:
     active(f(a(),X,X)) -> mark(f(X,b(),b()))
     active(b()) -> mark(a())
     mark(f(X1,X2,X3)) -> active(f(X1,mark(X2),X3))
     mark(a()) -> active(a())
     mark(b()) -> active(b())
     f(mark(X1),X2,X3) -> f(X1,X2,X3)
     f(X1,mark(X2),X3) -> f(X1,X2,X3)
     f(X1,X2,mark(X3)) -> f(X1,X2,X3)
     f(active(X1),X2,X3) -> f(X1,X2,X3)
     f(X1,active(X2),X3) -> f(X1,X2,X3)
     f(X1,X2,active(X3)) -> f(X1,X2,X3)
    SCC Processor:
     #sccs: 2
     #rules: 9
     #arcs: 56/196
     DPs:
      mark#(f(X1,X2,X3)) -> mark#(X2)
      mark#(f(X1,X2,X3)) -> active#(f(X1,mark(X2),X3))
      active#(f(a(),X,X)) -> mark#(f(X,b(),b()))
     TRS:
      active(f(a(),X,X)) -> mark(f(X,b(),b()))
      active(b()) -> mark(a())
      mark(f(X1,X2,X3)) -> active(f(X1,mark(X2),X3))
      mark(a()) -> active(a())
      mark(b()) -> active(b())
      f(mark(X1),X2,X3) -> f(X1,X2,X3)
      f(X1,mark(X2),X3) -> f(X1,X2,X3)
      f(X1,X2,mark(X3)) -> f(X1,X2,X3)
      f(active(X1),X2,X3) -> f(X1,X2,X3)
      f(X1,active(X2),X3) -> f(X1,X2,X3)
      f(X1,X2,active(X3)) -> f(X1,X2,X3)
     Open
     
     DPs:
      f#(X1,X2,active(X3)) -> f#(X1,X2,X3)
      f#(X1,active(X2),X3) -> f#(X1,X2,X3)
      f#(active(X1),X2,X3) -> f#(X1,X2,X3)
      f#(X1,X2,mark(X3)) -> f#(X1,X2,X3)
      f#(X1,mark(X2),X3) -> f#(X1,X2,X3)
      f#(mark(X1),X2,X3) -> f#(X1,X2,X3)
     TRS:
      active(f(a(),X,X)) -> mark(f(X,b(),b()))
      active(b()) -> mark(a())
      mark(f(X1,X2,X3)) -> active(f(X1,mark(X2),X3))
      mark(a()) -> active(a())
      mark(b()) -> active(b())
      f(mark(X1),X2,X3) -> f(X1,X2,X3)
      f(X1,mark(X2),X3) -> f(X1,X2,X3)
      f(X1,X2,mark(X3)) -> f(X1,X2,X3)
      f(active(X1),X2,X3) -> f(X1,X2,X3)
      f(X1,active(X2),X3) -> f(X1,X2,X3)
      f(X1,X2,active(X3)) -> f(X1,X2,X3)
     Open