MAYBE
Time: 0.001334
TRS:
 {      f(x, 0()) -> x,
    f(f(x, y), z) -> f(x, f(y, z)),
        f(0(), y) -> y,
        f(i x, y) -> i x,
    f(g(x, y), z) -> g(f(x, z), f(y, z)),
  f(1(), g(x, y)) -> x,
  f(2(), g(x, y)) -> y}
 DP:
  DP:
   {f#(f(x, y), z) -> f#(y, z),
    f#(f(x, y), z) -> f#(x, f(y, z)),
    f#(g(x, y), z) -> f#(y, z),
    f#(g(x, y), z) -> f#(x, z)}
  TRS:
  {      f(x, 0()) -> x,
     f(f(x, y), z) -> f(x, f(y, z)),
         f(0(), y) -> y,
         f(i x, y) -> i x,
     f(g(x, y), z) -> g(f(x, z), f(y, z)),
   f(1(), g(x, y)) -> x,
   f(2(), g(x, y)) -> y}
  UR:
   {      f(x, 0()) -> x,
      f(f(x, y), z) -> f(x, f(y, z)),
          f(0(), y) -> y,
          f(i x, y) -> i x,
      f(g(x, y), z) -> g(f(x, z), f(y, z)),
    f(1(), g(x, y)) -> x,
    f(2(), g(x, y)) -> y,
            a(w, v) -> w,
            a(w, v) -> v}
   EDG:
    {(f#(f(x, y), z) -> f#(x, f(y, z)), f#(g(x, y), z) -> f#(x, z))
     (f#(f(x, y), z) -> f#(x, f(y, z)), f#(g(x, y), z) -> f#(y, z))
     (f#(f(x, y), z) -> f#(x, f(y, z)), f#(f(x, y), z) -> f#(x, f(y, z)))
     (f#(f(x, y), z) -> f#(x, f(y, z)), f#(f(x, y), z) -> f#(y, z))
     (f#(g(x, y), z) -> f#(x, z), f#(g(x, y), z) -> f#(x, z))
     (f#(g(x, y), z) -> f#(x, z), f#(g(x, y), z) -> f#(y, z))
     (f#(g(x, y), z) -> f#(x, z), f#(f(x, y), z) -> f#(x, f(y, z)))
     (f#(g(x, y), z) -> f#(x, z), f#(f(x, y), z) -> f#(y, z))
     (f#(g(x, y), z) -> f#(y, z), f#(f(x, y), z) -> f#(y, z))
     (f#(g(x, y), z) -> f#(y, z), f#(f(x, y), z) -> f#(x, f(y, z)))
     (f#(g(x, y), z) -> f#(y, z), f#(g(x, y), z) -> f#(y, z))
     (f#(g(x, y), z) -> f#(y, z), f#(g(x, y), z) -> f#(x, z))
     (f#(f(x, y), z) -> f#(y, z), f#(f(x, y), z) -> f#(y, z))
     (f#(f(x, y), z) -> f#(y, z), f#(f(x, y), z) -> f#(x, f(y, z)))
     (f#(f(x, y), z) -> f#(y, z), f#(g(x, y), z) -> f#(y, z))
     (f#(f(x, y), z) -> f#(y, z), f#(g(x, y), z) -> f#(x, z))}
    STATUS:
     arrows: 0.000000
     SCCS (1):
      Scc:
       {f#(f(x, y), z) -> f#(y, z),
        f#(f(x, y), z) -> f#(x, f(y, z)),
        f#(g(x, y), z) -> f#(y, z),
        f#(g(x, y), z) -> f#(x, z)}
      
      SCC (4):
       Strict:
        {f#(f(x, y), z) -> f#(y, z),
         f#(f(x, y), z) -> f#(x, f(y, z)),
         f#(g(x, y), z) -> f#(y, z),
         f#(g(x, y), z) -> f#(x, z)}
       Weak:
       {      f(x, 0()) -> x,
          f(f(x, y), z) -> f(x, f(y, z)),
              f(0(), y) -> y,
              f(i x, y) -> i x,
          f(g(x, y), z) -> g(f(x, z), f(y, z)),
        f(1(), g(x, y)) -> x,
        f(2(), g(x, y)) -> y}
       Open