MAYBE
Time: 0.002661
TRS:
 {          g(x, x) -> g(a(), 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, x) -> g#(a(), 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, x) -> g(a(), 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()))}
  UR:
   {          g(x, x) -> g(a(), 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:
    {(g#(d(), g(d(), x)) -> g#(c(), g(e(), x)), g#(c(), g(c(), x)) -> g#(d(), x))
     (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#(x, x) -> g#(a(), b()))
     (f# g(x, y) -> g#(f f x, a()), g#(x, x) -> g#(a(), b()))
     (g#(e(), g(e(), x)) -> g#(c(), x), g#(c(), g(c(), x)) -> 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#(c(), x), g#(x, x) -> g#(a(), b()))
     (g#(c(), g(c(), x)) -> g#(d(), x), g#(d(), g(d(), x)) -> g#(c(), g(e(), x)))
     (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#(x, x) -> g#(a(), 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#(e(), x), g#(x, x) -> g#(a(), b()))
     (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#(e(), g(e(), x)) -> g#(c(), x))
     (f# g(x, y) -> g#(y, g(f f x, a())), g#(x, x) -> g#(a(), b()))
     (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#(e(), g(d(), x)), g#(x, x) -> g#(a(), b()))
     (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#(e(), g(e(), x)) -> g#(c(), x))
     (g#(e(), g(e(), x)) -> g#(d(), g(c(), x)), g#(x, x) -> g#(a(), b()))
     (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#(d(), g(d(), x)) -> g#(c(), g(e(), x)))
     (f# g(x, y) -> f# x, f# g(x, y) -> g#(y, g(f f x, a())))
     (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) -> f# x)
     (f# g(x, y) -> f# x, f# g(x, y) -> f# f x)}
    STATUS:
     arrows: 0.719008
     SCCS (2):
      Scc:
       {f# g(x, y) -> f# x,
        f# g(x, y) -> f# f x}
      Scc:
       {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, x) -> g(a(), 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 (6):
       Strict:
        {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, x) -> g(a(), 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