MAYBE

Problem:
 a(a(a(b(b(x1))))) -> b(b(a(b(b(a(a(a(x1))))))))
 b(b(a(x1))) -> x1
 a(x1) -> b(b(b(x1)))
 a(x1) -> b(x1)

Proof:
 DP Processor:
  DPs:
   a#(a(a(b(b(x1))))) -> a#(x1)
   a#(a(a(b(b(x1))))) -> a#(a(x1))
   a#(a(a(b(b(x1))))) -> a#(a(a(x1)))
   a#(a(a(b(b(x1))))) -> b#(a(a(a(x1))))
   a#(a(a(b(b(x1))))) -> b#(b(a(a(a(x1)))))
   a#(a(a(b(b(x1))))) -> a#(b(b(a(a(a(x1))))))
   a#(a(a(b(b(x1))))) -> b#(a(b(b(a(a(a(x1)))))))
   a#(a(a(b(b(x1))))) -> b#(b(a(b(b(a(a(a(x1))))))))
   a#(x1) -> b#(x1)
   a#(x1) -> b#(b(x1))
   a#(x1) -> b#(b(b(x1)))
  TRS:
   a(a(a(b(b(x1))))) -> b(b(a(b(b(a(a(a(x1))))))))
   b(b(a(x1))) -> x1
   a(x1) -> b(b(b(x1)))
   a(x1) -> b(x1)
  TDG Processor:
   DPs:
    a#(a(a(b(b(x1))))) -> a#(x1)
    a#(a(a(b(b(x1))))) -> a#(a(x1))
    a#(a(a(b(b(x1))))) -> a#(a(a(x1)))
    a#(a(a(b(b(x1))))) -> b#(a(a(a(x1))))
    a#(a(a(b(b(x1))))) -> b#(b(a(a(a(x1)))))
    a#(a(a(b(b(x1))))) -> a#(b(b(a(a(a(x1))))))
    a#(a(a(b(b(x1))))) -> b#(a(b(b(a(a(a(x1)))))))
    a#(a(a(b(b(x1))))) -> b#(b(a(b(b(a(a(a(x1))))))))
    a#(x1) -> b#(x1)
    a#(x1) -> b#(b(x1))
    a#(x1) -> b#(b(b(x1)))
   TRS:
    a(a(a(b(b(x1))))) -> b(b(a(b(b(a(a(a(x1))))))))
    b(b(a(x1))) -> x1
    a(x1) -> b(b(b(x1)))
    a(x1) -> b(x1)
   graph:
    a#(a(a(b(b(x1))))) -> a#(a(a(x1))) -> a#(x1) -> b#(b(b(x1)))
    a#(a(a(b(b(x1))))) -> a#(a(a(x1))) -> a#(x1) -> b#(b(x1))
    a#(a(a(b(b(x1))))) -> a#(a(a(x1))) -> a#(x1) -> b#(x1)
    a#(a(a(b(b(x1))))) -> a#(a(a(x1))) ->
    a#(a(a(b(b(x1))))) -> b#(b(a(b(b(a(a(a(x1))))))))
    a#(a(a(b(b(x1))))) -> a#(a(a(x1))) ->
    a#(a(a(b(b(x1))))) -> b#(a(b(b(a(a(a(x1)))))))
    a#(a(a(b(b(x1))))) -> a#(a(a(x1))) ->
    a#(a(a(b(b(x1))))) -> a#(b(b(a(a(a(x1))))))
    a#(a(a(b(b(x1))))) -> a#(a(a(x1))) ->
    a#(a(a(b(b(x1))))) -> b#(b(a(a(a(x1)))))
    a#(a(a(b(b(x1))))) -> a#(a(a(x1))) ->
    a#(a(a(b(b(x1))))) -> b#(a(a(a(x1))))
    a#(a(a(b(b(x1))))) -> a#(a(a(x1))) ->
    a#(a(a(b(b(x1))))) -> a#(a(a(x1)))
    a#(a(a(b(b(x1))))) -> a#(a(a(x1))) ->
    a#(a(a(b(b(x1))))) -> a#(a(x1))
    a#(a(a(b(b(x1))))) -> a#(a(a(x1))) ->
    a#(a(a(b(b(x1))))) -> a#(x1)
    a#(a(a(b(b(x1))))) -> a#(a(x1)) -> a#(x1) -> b#(b(b(x1)))
    a#(a(a(b(b(x1))))) -> a#(a(x1)) -> a#(x1) -> b#(b(x1))
    a#(a(a(b(b(x1))))) -> a#(a(x1)) -> a#(x1) -> b#(x1)
    a#(a(a(b(b(x1))))) -> a#(a(x1)) ->
    a#(a(a(b(b(x1))))) -> b#(b(a(b(b(a(a(a(x1))))))))
    a#(a(a(b(b(x1))))) -> a#(a(x1)) ->
    a#(a(a(b(b(x1))))) -> b#(a(b(b(a(a(a(x1)))))))
    a#(a(a(b(b(x1))))) -> a#(a(x1)) ->
    a#(a(a(b(b(x1))))) -> a#(b(b(a(a(a(x1))))))
    a#(a(a(b(b(x1))))) -> a#(a(x1)) ->
    a#(a(a(b(b(x1))))) -> b#(b(a(a(a(x1)))))
    a#(a(a(b(b(x1))))) -> a#(a(x1)) ->
    a#(a(a(b(b(x1))))) -> b#(a(a(a(x1))))
    a#(a(a(b(b(x1))))) -> a#(a(x1)) ->
    a#(a(a(b(b(x1))))) -> a#(a(a(x1)))
    a#(a(a(b(b(x1))))) -> a#(a(x1)) ->
    a#(a(a(b(b(x1))))) -> a#(a(x1))
    a#(a(a(b(b(x1))))) -> a#(a(x1)) ->
    a#(a(a(b(b(x1))))) -> a#(x1)
    a#(a(a(b(b(x1))))) -> a#(b(b(a(a(a(x1)))))) ->
    a#(x1) -> b#(b(b(x1)))
    a#(a(a(b(b(x1))))) -> a#(b(b(a(a(a(x1)))))) ->
    a#(x1) -> b#(b(x1))
    a#(a(a(b(b(x1))))) -> a#(b(b(a(a(a(x1)))))) ->
    a#(x1) -> b#(x1)
    a#(a(a(b(b(x1))))) -> a#(b(b(a(a(a(x1)))))) ->
    a#(a(a(b(b(x1))))) -> b#(b(a(b(b(a(a(a(x1))))))))
    a#(a(a(b(b(x1))))) -> a#(b(b(a(a(a(x1)))))) ->
    a#(a(a(b(b(x1))))) -> b#(a(b(b(a(a(a(x1)))))))
    a#(a(a(b(b(x1))))) -> a#(b(b(a(a(a(x1)))))) ->
    a#(a(a(b(b(x1))))) -> a#(b(b(a(a(a(x1))))))
    a#(a(a(b(b(x1))))) -> a#(b(b(a(a(a(x1)))))) ->
    a#(a(a(b(b(x1))))) -> b#(b(a(a(a(x1)))))
    a#(a(a(b(b(x1))))) -> a#(b(b(a(a(a(x1)))))) ->
    a#(a(a(b(b(x1))))) -> b#(a(a(a(x1))))
    a#(a(a(b(b(x1))))) -> a#(b(b(a(a(a(x1)))))) ->
    a#(a(a(b(b(x1))))) -> a#(a(a(x1)))
    a#(a(a(b(b(x1))))) -> a#(b(b(a(a(a(x1)))))) ->
    a#(a(a(b(b(x1))))) -> a#(a(x1))
    a#(a(a(b(b(x1))))) -> a#(b(b(a(a(a(x1)))))) ->
    a#(a(a(b(b(x1))))) -> a#(x1)
    a#(a(a(b(b(x1))))) -> a#(x1) -> a#(x1) -> b#(b(b(x1)))
    a#(a(a(b(b(x1))))) -> a#(x1) -> a#(x1) -> b#(b(x1))
    a#(a(a(b(b(x1))))) -> a#(x1) -> a#(x1) -> b#(x1)
    a#(a(a(b(b(x1))))) -> a#(x1) ->
    a#(a(a(b(b(x1))))) -> b#(b(a(b(b(a(a(a(x1))))))))
    a#(a(a(b(b(x1))))) -> a#(x1) ->
    a#(a(a(b(b(x1))))) -> b#(a(b(b(a(a(a(x1)))))))
    a#(a(a(b(b(x1))))) -> a#(x1) ->
    a#(a(a(b(b(x1))))) -> a#(b(b(a(a(a(x1))))))
    a#(a(a(b(b(x1))))) -> a#(x1) ->
    a#(a(a(b(b(x1))))) -> b#(b(a(a(a(x1)))))
    a#(a(a(b(b(x1))))) -> a#(x1) ->
    a#(a(a(b(b(x1))))) -> b#(a(a(a(x1))))
    a#(a(a(b(b(x1))))) -> a#(x1) -> a#(a(a(b(b(x1))))) -> a#(a(a(x1)))
    a#(a(a(b(b(x1))))) -> a#(x1) -> a#(a(a(b(b(x1))))) -> a#(a(x1))
    a#(a(a(b(b(x1))))) -> a#(x1) -> a#(a(a(b(b(x1))))) -> a#(x1)
   SCC Processor:
    #sccs: 1
    #rules: 4
    #arcs: 44/121
    DPs:
     a#(a(a(b(b(x1))))) -> a#(a(a(x1)))
     a#(a(a(b(b(x1))))) -> a#(x1)
     a#(a(a(b(b(x1))))) -> a#(a(x1))
     a#(a(a(b(b(x1))))) -> a#(b(b(a(a(a(x1))))))
    TRS:
     a(a(a(b(b(x1))))) -> b(b(a(b(b(a(a(a(x1))))))))
     b(b(a(x1))) -> x1
     a(x1) -> b(b(b(x1)))
     a(x1) -> b(x1)
    Open