MAYBE

Problem:
 a(a(f(b(),a(x)))) -> f(a(a(a(x))),b())
 a(a(x)) -> f(b(),a(f(a(x),b())))
 f(a(x),b()) -> f(b(),a(x))

Proof:
 DP Processor:
  DPs:
   a#(a(f(b(),a(x)))) -> a#(a(x))
   a#(a(f(b(),a(x)))) -> a#(a(a(x)))
   a#(a(f(b(),a(x)))) -> f#(a(a(a(x))),b())
   a#(a(x)) -> f#(a(x),b())
   a#(a(x)) -> a#(f(a(x),b()))
   a#(a(x)) -> f#(b(),a(f(a(x),b())))
   f#(a(x),b()) -> f#(b(),a(x))
  TRS:
   a(a(f(b(),a(x)))) -> f(a(a(a(x))),b())
   a(a(x)) -> f(b(),a(f(a(x),b())))
   f(a(x),b()) -> f(b(),a(x))
  TDG Processor:
   DPs:
    a#(a(f(b(),a(x)))) -> a#(a(x))
    a#(a(f(b(),a(x)))) -> a#(a(a(x)))
    a#(a(f(b(),a(x)))) -> f#(a(a(a(x))),b())
    a#(a(x)) -> f#(a(x),b())
    a#(a(x)) -> a#(f(a(x),b()))
    a#(a(x)) -> f#(b(),a(f(a(x),b())))
    f#(a(x),b()) -> f#(b(),a(x))
   TRS:
    a(a(f(b(),a(x)))) -> f(a(a(a(x))),b())
    a(a(x)) -> f(b(),a(f(a(x),b())))
    f(a(x),b()) -> f(b(),a(x))
   graph:
    f#(a(x),b()) -> f#(b(),a(x)) ->
    f#(a(x),b()) -> f#(b(),a(x))
    a#(a(f(b(),a(x)))) -> f#(a(a(a(x))),b()) ->
    f#(a(x),b()) -> f#(b(),a(x))
    a#(a(f(b(),a(x)))) -> a#(a(a(x))) ->
    a#(a(x)) -> f#(b(),a(f(a(x),b())))
    a#(a(f(b(),a(x)))) -> a#(a(a(x))) ->
    a#(a(x)) -> a#(f(a(x),b()))
    a#(a(f(b(),a(x)))) -> a#(a(a(x))) -> a#(a(x)) -> f#(a(x),b())
    a#(a(f(b(),a(x)))) -> a#(a(a(x))) ->
    a#(a(f(b(),a(x)))) -> f#(a(a(a(x))),b())
    a#(a(f(b(),a(x)))) -> a#(a(a(x))) ->
    a#(a(f(b(),a(x)))) -> a#(a(a(x)))
    a#(a(f(b(),a(x)))) -> a#(a(a(x))) ->
    a#(a(f(b(),a(x)))) -> a#(a(x))
    a#(a(f(b(),a(x)))) -> a#(a(x)) ->
    a#(a(x)) -> f#(b(),a(f(a(x),b())))
    a#(a(f(b(),a(x)))) -> a#(a(x)) -> a#(a(x)) -> a#(f(a(x),b()))
    a#(a(f(b(),a(x)))) -> a#(a(x)) -> a#(a(x)) -> f#(a(x),b())
    a#(a(f(b(),a(x)))) -> a#(a(x)) ->
    a#(a(f(b(),a(x)))) -> f#(a(a(a(x))),b())
    a#(a(f(b(),a(x)))) -> a#(a(x)) ->
    a#(a(f(b(),a(x)))) -> a#(a(a(x)))
    a#(a(f(b(),a(x)))) -> a#(a(x)) -> a#(a(f(b(),a(x)))) -> a#(a(x))
    a#(a(x)) -> f#(a(x),b()) -> f#(a(x),b()) -> f#(b(),a(x))
    a#(a(x)) -> f#(b(),a(f(a(x),b()))) -> f#(a(x),b()) -> f#(b(),a(x))
    a#(a(x)) -> a#(f(a(x),b())) -> a#(a(x)) -> f#(b(),a(f(a(x),b())))
    a#(a(x)) -> a#(f(a(x),b())) -> a#(a(x)) -> a#(f(a(x),b()))
    a#(a(x)) -> a#(f(a(x),b())) -> a#(a(x)) -> f#(a(x),b())
    a#(a(x)) -> a#(f(a(x),b())) ->
    a#(a(f(b(),a(x)))) -> f#(a(a(a(x))),b())
    a#(a(x)) -> a#(f(a(x),b())) -> a#(a(f(b(),a(x)))) -> a#(a(a(x)))
    a#(a(x)) -> a#(f(a(x),b())) -> a#(a(f(b(),a(x)))) -> a#(a(x))
   EDG Processor:
    DPs:
     a#(a(f(b(),a(x)))) -> a#(a(x))
     a#(a(f(b(),a(x)))) -> a#(a(a(x)))
     a#(a(f(b(),a(x)))) -> f#(a(a(a(x))),b())
     a#(a(x)) -> f#(a(x),b())
     a#(a(x)) -> a#(f(a(x),b()))
     a#(a(x)) -> f#(b(),a(f(a(x),b())))
     f#(a(x),b()) -> f#(b(),a(x))
    TRS:
     a(a(f(b(),a(x)))) -> f(a(a(a(x))),b())
     a(a(x)) -> f(b(),a(f(a(x),b())))
     f(a(x),b()) -> f(b(),a(x))
    graph:
     a#(a(f(b(),a(x)))) -> f#(a(a(a(x))),b()) ->
     f#(a(x),b()) -> f#(b(),a(x))
     a#(a(f(b(),a(x)))) -> a#(a(a(x))) ->
     a#(a(f(b(),a(x)))) -> a#(a(x))
     a#(a(f(b(),a(x)))) -> a#(a(a(x))) ->
     a#(a(f(b(),a(x)))) -> a#(a(a(x)))
     a#(a(f(b(),a(x)))) -> a#(a(a(x))) ->
     a#(a(f(b(),a(x)))) -> f#(a(a(a(x))),b())
     a#(a(f(b(),a(x)))) -> a#(a(a(x))) -> a#(a(x)) -> f#(a(x),b())
     a#(a(f(b(),a(x)))) -> a#(a(a(x))) ->
     a#(a(x)) -> a#(f(a(x),b()))
     a#(a(f(b(),a(x)))) -> a#(a(a(x))) ->
     a#(a(x)) -> f#(b(),a(f(a(x),b())))
     a#(a(f(b(),a(x)))) -> a#(a(x)) -> a#(a(f(b(),a(x)))) -> a#(a(x))
     a#(a(f(b(),a(x)))) -> a#(a(x)) ->
     a#(a(f(b(),a(x)))) -> a#(a(a(x)))
     a#(a(f(b(),a(x)))) -> a#(a(x)) ->
     a#(a(f(b(),a(x)))) -> f#(a(a(a(x))),b())
     a#(a(f(b(),a(x)))) -> a#(a(x)) -> a#(a(x)) -> f#(a(x),b())
     a#(a(f(b(),a(x)))) -> a#(a(x)) -> a#(a(x)) -> a#(f(a(x),b()))
     a#(a(f(b(),a(x)))) -> a#(a(x)) -> a#(a(x)) -> f#(b(),a(f(a(x),b())))
     a#(a(x)) -> f#(a(x),b()) -> f#(a(x),b()) -> f#(b(),a(x))
    Restore Modifier:
     DPs:
      a#(a(f(b(),a(x)))) -> a#(a(x))
      a#(a(f(b(),a(x)))) -> a#(a(a(x)))
      a#(a(f(b(),a(x)))) -> f#(a(a(a(x))),b())
      a#(a(x)) -> f#(a(x),b())
      a#(a(x)) -> a#(f(a(x),b()))
      a#(a(x)) -> f#(b(),a(f(a(x),b())))
      f#(a(x),b()) -> f#(b(),a(x))
     TRS:
      a(a(f(b(),a(x)))) -> f(a(a(a(x))),b())
      a(a(x)) -> f(b(),a(f(a(x),b())))
      f(a(x),b()) -> f(b(),a(x))
     SCC Processor:
      #sccs: 1
      #rules: 2
      #arcs: 14/49
      DPs:
       a#(a(f(b(),a(x)))) -> a#(a(a(x)))
       a#(a(f(b(),a(x)))) -> a#(a(x))
      TRS:
       a(a(f(b(),a(x)))) -> f(a(a(a(x))),b())
       a(a(x)) -> f(b(),a(f(a(x),b())))
       f(a(x),b()) -> f(b(),a(x))
      Open