MAYBE
Time: 0.002404
TRS:
 {    f a() -> b(),
      f c() -> d(),
  f g(x, y) -> g(f x, f y),
  f h(x, y) -> g(h(y, f x), h(x, f y)),
    g(x, x) -> h(e(), x)}
 DP:
  DP:
   {f# g(x, y) -> f# x,
    f# g(x, y) -> f# y,
    f# g(x, y) -> g#(f x, f y),
    f# h(x, y) -> f# x,
    f# h(x, y) -> f# y,
    f# h(x, y) -> g#(h(y, f x), h(x, f y))}
  TRS:
  {    f a() -> b(),
       f c() -> d(),
   f g(x, y) -> g(f x, f y),
   f h(x, y) -> g(h(y, f x), h(x, f y)),
     g(x, x) -> h(e(), x)}
  UR:
   {    f a() -> b(),
        f c() -> d(),
    f g(x, y) -> g(f x, f y),
    f h(x, y) -> g(h(y, f x), h(x, f y)),
      g(x, x) -> h(e(), x),
      i(z, w) -> z,
      i(z, w) -> w}
   EDG:
    {(f# h(x, y) -> f# y, f# h(x, y) -> g#(h(y, f x), h(x, f y)))
     (f# h(x, y) -> f# y, f# h(x, y) -> f# y)
     (f# h(x, y) -> f# y, f# h(x, y) -> f# x)
     (f# h(x, y) -> f# y, f# g(x, y) -> g#(f x, f y))
     (f# h(x, y) -> f# y, f# g(x, y) -> f# y)
     (f# h(x, y) -> f# y, f# g(x, y) -> f# x)
     (f# h(x, y) -> f# x, f# h(x, y) -> g#(h(y, f x), h(x, f y)))
     (f# h(x, y) -> f# x, f# h(x, y) -> f# y)
     (f# h(x, y) -> f# x, f# h(x, y) -> f# x)
     (f# h(x, y) -> f# x, f# g(x, y) -> g#(f x, f y))
     (f# h(x, y) -> f# x, f# g(x, y) -> f# y)
     (f# h(x, y) -> f# x, f# g(x, y) -> f# x)
     (f# g(x, y) -> f# x, f# g(x, y) -> f# x)
     (f# g(x, y) -> f# x, f# g(x, y) -> f# y)
     (f# g(x, y) -> f# x, f# g(x, y) -> g#(f x, f y))
     (f# g(x, y) -> f# x, f# h(x, y) -> f# x)
     (f# g(x, y) -> f# x, f# h(x, y) -> f# y)
     (f# g(x, y) -> f# x, f# h(x, y) -> g#(h(y, f x), h(x, f y)))
     (f# g(x, y) -> f# y, f# g(x, y) -> f# x)
     (f# g(x, y) -> f# y, f# g(x, y) -> f# y)
     (f# g(x, y) -> f# y, f# g(x, y) -> g#(f x, f y))
     (f# g(x, y) -> f# y, f# h(x, y) -> f# x)
     (f# g(x, y) -> f# y, f# h(x, y) -> f# y)
     (f# g(x, y) -> f# y, f# h(x, y) -> g#(h(y, f x), h(x, f y)))}
    STATUS:
     arrows: 0.333333
     SCCS (1):
      Scc:
       {f# g(x, y) -> f# x,
        f# g(x, y) -> f# y,
        f# h(x, y) -> f# x,
        f# h(x, y) -> f# y}
      
      SCC (4):
       Strict:
        {f# g(x, y) -> f# x,
         f# g(x, y) -> f# y,
         f# h(x, y) -> f# x,
         f# h(x, y) -> f# y}
       Weak:
       {    f a() -> b(),
            f c() -> d(),
        f g(x, y) -> g(f x, f y),
        f h(x, y) -> g(h(y, f x), h(x, f y)),
          g(x, x) -> h(e(), x)}
       Open