MAYBE

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

Proof:
 DP Processor:
  DPs:
   f#(x,a(b(y))) -> f#(a(a(x)),y)
   f#(x,b(a(y))) -> f#(b(b(x)),y)
   f#(a(x),y) -> f#(x,a(y))
   f#(b(x),y) -> f#(x,b(y))
  TRS:
   f(x,a(b(y))) -> f(a(a(x)),y)
   f(x,b(a(y))) -> f(b(b(x)),y)
   f(a(x),y) -> f(x,a(y))
   f(b(x),y) -> f(x,b(y))
  Usable Rule Processor:
   DPs:
    f#(x,a(b(y))) -> f#(a(a(x)),y)
    f#(x,b(a(y))) -> f#(b(b(x)),y)
    f#(a(x),y) -> f#(x,a(y))
    f#(b(x),y) -> f#(x,b(y))
   TRS:
    
   ADG Processor:
    DPs:
     f#(x,a(b(y))) -> f#(a(a(x)),y)
     f#(x,b(a(y))) -> f#(b(b(x)),y)
     f#(a(x),y) -> f#(x,a(y))
     f#(b(x),y) -> f#(x,b(y))
    TRS:
     
    graph:
     f#(a(x),y) -> f#(x,a(y)) -> f#(x,a(b(y))) -> f#(a(a(x)),y)
     f#(a(x),y) -> f#(x,a(y)) -> f#(a(x),y) -> f#(x,a(y))
     f#(a(x),y) -> f#(x,a(y)) -> f#(b(x),y) -> f#(x,b(y))
     f#(b(x),y) -> f#(x,b(y)) -> f#(x,b(a(y))) -> f#(b(b(x)),y)
     f#(b(x),y) -> f#(x,b(y)) -> f#(a(x),y) -> f#(x,a(y))
     f#(b(x),y) -> f#(x,b(y)) -> f#(b(x),y) -> f#(x,b(y))
     f#(x,a(b(y))) -> f#(a(a(x)),y) -> f#(x,a(b(y))) -> f#(a(a(x)),y)
     f#(x,a(b(y))) -> f#(a(a(x)),y) -> f#(x,b(a(y))) -> f#(b(b(x)),y)
     f#(x,a(b(y))) -> f#(a(a(x)),y) -> f#(a(x),y) -> f#(x,a(y))
     f#(x,b(a(y))) -> f#(b(b(x)),y) -> f#(x,a(b(y))) -> f#(a(a(x)),y)
     f#(x,b(a(y))) -> f#(b(b(x)),y) -> f#(x,b(a(y))) -> f#(b(b(x)),y)
     f#(x,b(a(y))) -> f#(b(b(x)),y) -> f#(b(x),y) -> f#(x,b(y))
    Restore Modifier:
     DPs:
      f#(x,a(b(y))) -> f#(a(a(x)),y)
      f#(x,b(a(y))) -> f#(b(b(x)),y)
      f#(a(x),y) -> f#(x,a(y))
      f#(b(x),y) -> f#(x,b(y))
     TRS:
      f(x,a(b(y))) -> f(a(a(x)),y)
      f(x,b(a(y))) -> f(b(b(x)),y)
      f(a(x),y) -> f(x,a(y))
      f(b(x),y) -> f(x,b(y))
     SCC Processor:
      #sccs: 1
      #rules: 4
      #arcs: 12/16
      DPs:
       f#(a(x),y) -> f#(x,a(y))
       f#(b(x),y) -> f#(x,b(y))
       f#(x,b(a(y))) -> f#(b(b(x)),y)
       f#(x,a(b(y))) -> f#(a(a(x)),y)
      TRS:
       f(x,a(b(y))) -> f(a(a(x)),y)
       f(x,b(a(y))) -> f(b(b(x)),y)
       f(a(x),y) -> f(x,a(y))
       f(b(x),y) -> f(x,b(y))
      Open