MAYBE
Time: 0.003626
TRS:
 {g(x, g(y, g(x, y))) -> g(a(), g(x, g(y, b()))),
    g(e(), g(e(), x)) -> g(d(), g(c(), x)),
    g(d(), g(d(), x)) -> g(c(), g(e(), x)),
    g(c(), g(c(), x)) -> g(e(), g(d(), x)),
            f g(x, y) -> g(y, g(f f x, a()))}
 DP:
  DP:
   {g#(x, g(y, g(x, y))) -> g#(x, g(y, b())),
    g#(x, g(y, g(x, y))) -> g#(y, b()),
    g#(x, g(y, g(x, y))) -> g#(a(), g(x, g(y, b()))),
      g#(e(), g(e(), x)) -> g#(d(), g(c(), x)),
      g#(e(), g(e(), x)) -> g#(c(), x),
      g#(d(), g(d(), x)) -> g#(e(), x),
      g#(d(), g(d(), x)) -> g#(c(), g(e(), x)),
      g#(c(), g(c(), x)) -> g#(e(), g(d(), x)),
      g#(c(), g(c(), x)) -> g#(d(), x),
              f# g(x, y) -> g#(y, g(f f x, a())),
              f# g(x, y) -> g#(f f x, a()),
              f# g(x, y) -> f# x,
              f# g(x, y) -> f# f x}
  TRS:
  {g(x, g(y, g(x, y))) -> g(a(), g(x, g(y, b()))),
     g(e(), g(e(), x)) -> g(d(), g(c(), x)),
     g(d(), g(d(), x)) -> g(c(), g(e(), x)),
     g(c(), g(c(), x)) -> g(e(), g(d(), x)),
             f g(x, y) -> g(y, g(f f x, a()))}
  EDG:
   {(f# g(x, y) -> f# x, f# g(x, y) -> f# f x)
    (f# g(x, y) -> f# x, f# g(x, y) -> f# x)
    (f# g(x, y) -> f# x, f# g(x, y) -> g#(f f x, a()))
    (f# g(x, y) -> f# x, f# g(x, y) -> g#(y, g(f f x, a())))
    (g#(d(), g(d(), x)) -> g#(e(), x), g#(e(), g(e(), x)) -> g#(c(), x))
    (g#(d(), g(d(), x)) -> g#(e(), x), g#(e(), g(e(), x)) -> g#(d(), g(c(), x)))
    (g#(d(), g(d(), x)) -> g#(e(), x), g#(x, g(y, g(x, y))) -> g#(a(), g(x, g(y, b()))))
    (g#(d(), g(d(), x)) -> g#(e(), x), g#(x, g(y, g(x, y))) -> g#(y, b()))
    (g#(d(), g(d(), x)) -> g#(e(), x), g#(x, g(y, g(x, y))) -> g#(x, g(y, b())))
    (g#(x, g(y, g(x, y))) -> g#(x, g(y, b())), g#(c(), g(c(), x)) -> g#(d(), x))
    (g#(x, g(y, g(x, y))) -> g#(x, g(y, b())), g#(c(), g(c(), x)) -> g#(e(), g(d(), x)))
    (g#(x, g(y, g(x, y))) -> g#(x, g(y, b())), g#(d(), g(d(), x)) -> g#(c(), g(e(), x)))
    (g#(x, g(y, g(x, y))) -> g#(x, g(y, b())), g#(d(), g(d(), x)) -> g#(e(), x))
    (g#(x, g(y, g(x, y))) -> g#(x, g(y, b())), g#(e(), g(e(), x)) -> g#(c(), x))
    (g#(x, g(y, g(x, y))) -> g#(x, g(y, b())), g#(e(), g(e(), x)) -> g#(d(), g(c(), x)))
    (g#(e(), g(e(), x)) -> g#(d(), g(c(), x)), g#(d(), g(d(), x)) -> g#(c(), g(e(), x)))
    (g#(e(), g(e(), x)) -> g#(d(), g(c(), x)), g#(d(), g(d(), x)) -> g#(e(), x))
    (g#(e(), g(e(), x)) -> g#(d(), g(c(), x)), g#(x, g(y, g(x, y))) -> g#(a(), g(x, g(y, b()))))
    (g#(e(), g(e(), x)) -> g#(d(), g(c(), x)), g#(x, g(y, g(x, y))) -> g#(y, b()))
    (g#(e(), g(e(), x)) -> g#(d(), g(c(), x)), g#(x, g(y, g(x, y))) -> g#(x, g(y, b())))
    (g#(c(), g(c(), x)) -> g#(e(), g(d(), x)), g#(e(), g(e(), x)) -> g#(c(), x))
    (g#(c(), g(c(), x)) -> g#(e(), g(d(), x)), g#(e(), g(e(), x)) -> g#(d(), g(c(), x)))
    (g#(c(), g(c(), x)) -> g#(e(), g(d(), x)), g#(x, g(y, g(x, y))) -> g#(a(), g(x, g(y, b()))))
    (g#(c(), g(c(), x)) -> g#(e(), g(d(), x)), g#(x, g(y, g(x, y))) -> g#(y, b()))
    (g#(c(), g(c(), x)) -> g#(e(), g(d(), x)), g#(x, g(y, g(x, y))) -> g#(x, g(y, b())))
    (f# g(x, y) -> f# f x, f# g(x, y) -> g#(y, g(f f x, a())))
    (f# g(x, y) -> f# f x, f# g(x, y) -> g#(f f x, a()))
    (f# g(x, y) -> f# f x, f# g(x, y) -> f# x)
    (f# g(x, y) -> f# f x, f# g(x, y) -> f# f x)
    (g#(d(), g(d(), x)) -> g#(c(), g(e(), x)), g#(x, g(y, g(x, y))) -> g#(x, g(y, b())))
    (g#(d(), g(d(), x)) -> g#(c(), g(e(), x)), g#(x, g(y, g(x, y))) -> g#(y, b()))
    (g#(d(), g(d(), x)) -> g#(c(), g(e(), x)), g#(x, g(y, g(x, y))) -> g#(a(), g(x, g(y, b()))))
    (g#(d(), g(d(), x)) -> g#(c(), g(e(), x)), g#(c(), g(c(), x)) -> g#(e(), g(d(), x)))
    (g#(d(), g(d(), x)) -> g#(c(), g(e(), x)), g#(c(), g(c(), x)) -> g#(d(), x))
    (f# g(x, y) -> g#(y, g(f f x, a())), g#(e(), g(e(), x)) -> g#(d(), g(c(), x)))
    (f# g(x, y) -> g#(y, g(f f x, a())), g#(e(), g(e(), x)) -> g#(c(), x))
    (f# g(x, y) -> g#(y, g(f f x, a())), g#(d(), g(d(), x)) -> g#(e(), x))
    (f# g(x, y) -> g#(y, g(f f x, a())), g#(d(), g(d(), x)) -> g#(c(), g(e(), x)))
    (f# g(x, y) -> g#(y, g(f f x, a())), g#(c(), g(c(), x)) -> g#(e(), g(d(), x)))
    (f# g(x, y) -> g#(y, g(f f x, a())), g#(c(), g(c(), x)) -> g#(d(), x))
    (g#(c(), g(c(), x)) -> g#(d(), x), g#(x, g(y, g(x, y))) -> g#(x, g(y, b())))
    (g#(c(), g(c(), x)) -> g#(d(), x), g#(x, g(y, g(x, y))) -> g#(y, b()))
    (g#(c(), g(c(), x)) -> g#(d(), x), g#(x, g(y, g(x, y))) -> g#(a(), g(x, g(y, b()))))
    (g#(c(), g(c(), x)) -> g#(d(), x), g#(d(), g(d(), x)) -> g#(e(), x))
    (g#(c(), g(c(), x)) -> g#(d(), x), g#(d(), g(d(), x)) -> g#(c(), g(e(), x)))
    (g#(e(), g(e(), x)) -> g#(c(), x), g#(x, g(y, g(x, y))) -> g#(x, g(y, b())))
    (g#(e(), g(e(), x)) -> g#(c(), x), g#(x, g(y, g(x, y))) -> g#(y, b()))
    (g#(e(), g(e(), x)) -> g#(c(), x), g#(x, g(y, g(x, y))) -> g#(a(), g(x, g(y, b()))))
    (g#(e(), g(e(), x)) -> g#(c(), x), g#(c(), g(c(), x)) -> g#(e(), g(d(), x)))
    (g#(e(), g(e(), x)) -> g#(c(), x), g#(c(), g(c(), x)) -> g#(d(), x))
    (g#(x, g(y, g(x, y))) -> g#(a(), g(x, g(y, b()))), g#(x, g(y, g(x, y))) -> g#(x, g(y, b())))
    (g#(x, g(y, g(x, y))) -> g#(a(), g(x, g(y, b()))), g#(x, g(y, g(x, y))) -> g#(y, b()))
    (g#(x, g(y, g(x, y))) -> g#(a(), g(x, g(y, b()))), g#(x, g(y, g(x, y))) -> g#(a(), g(x, g(y, b()))))}
   STATUS:
    arrows: 0.686391
    SCCS (2):
     Scc:
      {f# g(x, y) -> f# x,
       f# g(x, y) -> f# f x}
     Scc:
      {g#(x, g(y, g(x, y))) -> g#(x, g(y, b())),
       g#(x, g(y, g(x, y))) -> g#(a(), g(x, g(y, b()))),
         g#(e(), g(e(), x)) -> g#(d(), g(c(), x)),
         g#(e(), g(e(), x)) -> g#(c(), x),
         g#(d(), g(d(), x)) -> g#(e(), x),
         g#(d(), g(d(), x)) -> g#(c(), g(e(), x)),
         g#(c(), g(c(), x)) -> g#(e(), g(d(), x)),
         g#(c(), g(c(), x)) -> g#(d(), x)}
     
     SCC (2):
      Strict:
       {f# g(x, y) -> f# x,
        f# g(x, y) -> f# f x}
      Weak:
      {g(x, g(y, g(x, y))) -> g(a(), g(x, g(y, b()))),
         g(e(), g(e(), x)) -> g(d(), g(c(), x)),
         g(d(), g(d(), x)) -> g(c(), g(e(), x)),
         g(c(), g(c(), x)) -> g(e(), g(d(), x)),
                 f g(x, y) -> g(y, g(f f x, a()))}
      Open
     
     
     SCC (8):
      Strict:
       {g#(x, g(y, g(x, y))) -> g#(x, g(y, b())),
        g#(x, g(y, g(x, y))) -> g#(a(), g(x, g(y, b()))),
          g#(e(), g(e(), x)) -> g#(d(), g(c(), x)),
          g#(e(), g(e(), x)) -> g#(c(), x),
          g#(d(), g(d(), x)) -> g#(e(), x),
          g#(d(), g(d(), x)) -> g#(c(), g(e(), x)),
          g#(c(), g(c(), x)) -> g#(e(), g(d(), x)),
          g#(c(), g(c(), x)) -> g#(d(), x)}
      Weak:
      {g(x, g(y, g(x, y))) -> g(a(), g(x, g(y, b()))),
         g(e(), g(e(), x)) -> g(d(), g(c(), x)),
         g(d(), g(d(), x)) -> g(c(), g(e(), x)),
         g(c(), g(c(), x)) -> g(e(), g(d(), x)),
                 f g(x, y) -> g(y, g(f f x, a()))}
      Open