YES

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)
  TDG 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#(b()) -> active#(b()) ->
    active#(f(a(),X,X)) -> mark#(f(X,b(),b()))
    mark#(b()) -> active#(b()) ->
    active#(f(a(),X,X)) -> f#(X,b(),b())
    mark#(f(X1,X2,X3)) -> mark#(X2) -> mark#(b()) -> active#(b())
    mark#(f(X1,X2,X3)) -> mark#(X2) -> mark#(a()) -> active#(a())
    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#(f(X1,X2,X3)) -> f#(X1,mark(X2),X3)
    mark#(f(X1,X2,X3)) -> mark#(X2) ->
    mark#(f(X1,X2,X3)) -> mark#(X2)
    mark#(f(X1,X2,X3)) -> f#(X1,mark(X2),X3) ->
    f#(X1,X2,active(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#(active(X1),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#(X1,mark(X2),X3) -> f#(X1,X2,X3)
    mark#(f(X1,X2,X3)) -> f#(X1,mark(X2),X3) ->
    f#(mark(X1),X2,X3) -> f#(X1,X2,X3)
    mark#(f(X1,X2,X3)) -> active#(f(X1,mark(X2),X3)) ->
    active#(b()) -> mark#(a())
    mark#(f(X1,X2,X3)) -> active#(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())
    mark#(a()) -> active#(a()) -> active#(b()) -> mark#(a())
    mark#(a()) -> active#(a()) ->
    active#(f(a(),X,X)) -> mark#(f(X,b(),b()))
    mark#(a()) -> active#(a()) ->
    active#(f(a(),X,X)) -> f#(X,b(),b())
    f#(mark(X1),X2,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,active(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#(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#(X1,mark(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#(active(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#(X1,active(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#(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#(X1,mark(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,mark(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,active(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,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#(X1,mark(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,active(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,active(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,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#(X1,mark(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,mark(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,active(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,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#(X1,mark(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#(X1,X2,active(X3)) -> f#(X1,X2,X3) ->
    f#(X1,X2,active(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#(active(X1),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#(X1,mark(X2),X3) -> f#(X1,X2,X3)
    f#(X1,X2,active(X3)) -> f#(X1,X2,X3) ->
    f#(mark(X1),X2,X3) -> f#(X1,X2,X3)
    active#(b()) -> mark#(a()) -> mark#(b()) -> active#(b())
    active#(b()) -> mark#(a()) -> mark#(a()) -> active#(a())
    active#(b()) -> mark#(a()) ->
    mark#(f(X1,X2,X3)) -> active#(f(X1,mark(X2),X3))
    active#(b()) -> mark#(a()) ->
    mark#(f(X1,X2,X3)) -> f#(X1,mark(X2),X3)
    active#(b()) -> mark#(a()) ->
    mark#(f(X1,X2,X3)) -> mark#(X2)
    active#(f(a(),X,X)) -> mark#(f(X,b(),b())) ->
    mark#(b()) -> active#(b())
    active#(f(a(),X,X)) -> mark#(f(X,b(),b())) ->
    mark#(a()) -> active#(a())
    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)) -> 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)) -> mark#(X2)
    active#(f(a(),X,X)) -> f#(X,b(),b()) ->
    f#(X1,X2,active(X3)) -> f#(X1,X2,X3)
    active#(f(a(),X,X)) -> f#(X,b(),b()) ->
    f#(X1,active(X2),X3) -> f#(X1,X2,X3)
    active#(f(a(),X,X)) -> f#(X,b(),b()) ->
    f#(active(X1),X2,X3) -> f#(X1,X2,X3)
    active#(f(a(),X,X)) -> f#(X,b(),b()) ->
    f#(X1,X2,mark(X3)) -> f#(X1,X2,X3)
    active#(f(a(),X,X)) -> f#(X,b(),b()) ->
    f#(X1,mark(X2),X3) -> f#(X1,X2,X3)
    active#(f(a(),X,X)) -> f#(X,b(),b()) -> f#(mark(X1),X2,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)
    CDG 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#(b()) -> active#(b())
      mark#(f(X1,X2,X3)) -> mark#(X2) -> mark#(a()) -> active#(a())
      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#(f(X1,X2,X3)) -> f#(X1,mark(X2),X3)
      mark#(f(X1,X2,X3)) -> mark#(X2) ->
      mark#(f(X1,X2,X3)) -> mark#(X2)
      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,mark(X2),X3) -> f#(X1,X2,X3)
      mark#(f(X1,X2,X3)) -> active#(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())
      active#(b()) -> mark#(a()) ->
      mark#(a()) -> active#(a())
      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)) -> 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)) -> mark#(X2)
     SCC Processor:
      #sccs: 1
      #rules: 3
      #arcs: 14/196
      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)
      Matrix Interpretation Processor: dim=3
       
       interpretation:
        [mark#](x0) = [1 1 1]x0 + [1],
        
        [active#](x0) = [1 1 1]x0,
        
                     [1 1 1]  
        [mark](x0) = [0 0 0]x0
                     [0 0 0]  ,
        
              [0]
        [b] = [1]
              [0],
        
                       [1 1 1]  
        [active](x0) = [0 0 0]x0
                       [0 0 0]  ,
        
                          [1 0 0]     [0 0 0]     [1 0 0]     [0]
        [f](x0, x1, x2) = [1 0 0]x0 + [1 1 1]x1 + [1 0 0]x2 + [1]
                          [1 0 0]     [0 0 0]     [0 0 0]     [0],
        
              [1]
        [a] = [0]
              [0]
       orientation:
        mark#(f(X1,X2,X3)) = [3 0 0]X1 + [1 1 1]X2 + [2 0 0]X3 + [2] >= [1 1 1]X2 + [1] = mark#(X2)
        
        mark#(f(X1,X2,X3)) = [3 0 0]X1 + [1 1 1]X2 + [2 0 0]X3 + [2] >= [3 0 0]X1 + [1 1 1]X2 + [2 0 0]X3 + [1] = active#(f(X1,mark(X2),X3))
        
        active#(f(a(),X,X)) = [3 1 1]X + [4] >= [3 0 0]X + [3] = mark#(f(X,b(),b()))
        
                             [3 1 1]    [4]    [3 0 0]    [2]                     
        active(f(a(),X,X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = mark(f(X,b(),b()))
                             [0 0 0]    [0]    [0 0 0]    [0]                     
        
                      [1]    [1]            
        active(b()) = [0] >= [0] = mark(a())
                      [0]    [0]            
        
                            [3 0 0]     [1 1 1]     [2 0 0]     [1]    [3 0 0]     [1 1 1]     [2 0 0]     [1]                            
        mark(f(X1,X2,X3)) = [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 + [0] = active(f(X1,mark(X2),X3))
                            [0 0 0]     [0 0 0]     [0 0 0]     [0]    [0 0 0]     [0 0 0]     [0 0 0]     [0]                            
        
                    [1]    [1]              
        mark(a()) = [0] >= [0] = active(a())
                    [0]    [0]              
        
                    [1]    [1]              
        mark(b()) = [0] >= [0] = active(b())
                    [0]    [0]              
        
                            [1 1 1]     [0 0 0]     [1 0 0]     [0]    [1 0 0]     [0 0 0]     [1 0 0]     [0]              
        f(mark(X1),X2,X3) = [1 1 1]X1 + [1 1 1]X2 + [1 0 0]X3 + [1] >= [1 0 0]X1 + [1 1 1]X2 + [1 0 0]X3 + [1] = f(X1,X2,X3)
                            [1 1 1]     [0 0 0]     [0 0 0]     [0]    [1 0 0]     [0 0 0]     [0 0 0]     [0]              
        
                            [1 0 0]     [0 0 0]     [1 0 0]     [0]    [1 0 0]     [0 0 0]     [1 0 0]     [0]              
        f(X1,mark(X2),X3) = [1 0 0]X1 + [1 1 1]X2 + [1 0 0]X3 + [1] >= [1 0 0]X1 + [1 1 1]X2 + [1 0 0]X3 + [1] = f(X1,X2,X3)
                            [1 0 0]     [0 0 0]     [0 0 0]     [0]    [1 0 0]     [0 0 0]     [0 0 0]     [0]              
        
                            [1 0 0]     [0 0 0]     [1 1 1]     [0]    [1 0 0]     [0 0 0]     [1 0 0]     [0]              
        f(X1,X2,mark(X3)) = [1 0 0]X1 + [1 1 1]X2 + [1 1 1]X3 + [1] >= [1 0 0]X1 + [1 1 1]X2 + [1 0 0]X3 + [1] = f(X1,X2,X3)
                            [1 0 0]     [0 0 0]     [0 0 0]     [0]    [1 0 0]     [0 0 0]     [0 0 0]     [0]              
        
                              [1 1 1]     [0 0 0]     [1 0 0]     [0]    [1 0 0]     [0 0 0]     [1 0 0]     [0]              
        f(active(X1),X2,X3) = [1 1 1]X1 + [1 1 1]X2 + [1 0 0]X3 + [1] >= [1 0 0]X1 + [1 1 1]X2 + [1 0 0]X3 + [1] = f(X1,X2,X3)
                              [1 1 1]     [0 0 0]     [0 0 0]     [0]    [1 0 0]     [0 0 0]     [0 0 0]     [0]              
        
                              [1 0 0]     [0 0 0]     [1 0 0]     [0]    [1 0 0]     [0 0 0]     [1 0 0]     [0]              
        f(X1,active(X2),X3) = [1 0 0]X1 + [1 1 1]X2 + [1 0 0]X3 + [1] >= [1 0 0]X1 + [1 1 1]X2 + [1 0 0]X3 + [1] = f(X1,X2,X3)
                              [1 0 0]     [0 0 0]     [0 0 0]     [0]    [1 0 0]     [0 0 0]     [0 0 0]     [0]              
        
                              [1 0 0]     [0 0 0]     [1 1 1]     [0]    [1 0 0]     [0 0 0]     [1 0 0]     [0]              
        f(X1,X2,active(X3)) = [1 0 0]X1 + [1 1 1]X2 + [1 1 1]X3 + [1] >= [1 0 0]X1 + [1 1 1]X2 + [1 0 0]X3 + [1] = f(X1,X2,X3)
                              [1 0 0]     [0 0 0]     [0 0 0]     [0]    [1 0 0]     [0 0 0]     [0 0 0]     [0]              
       problem:
        DPs:
         
        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)
       Qed