MAYBE
Time: 0.054834
TRS:
 {f(f(a(), x), a()) -> f(f(f(x, a()), f(a(), a())), a())}
 DP:
  DP:
   {f#(f(a(), x), a()) -> f#(x, a()),
    f#(f(a(), x), a()) -> f#(f(x, a()), f(a(), a())),
    f#(f(a(), x), a()) -> f#(f(f(x, a()), f(a(), a())), a()),
    f#(f(a(), x), a()) -> f#(a(), a())}
  TRS:
  {f(f(a(), x), a()) -> f(f(f(x, a()), f(a(), a())), a())}
  UR:
   {f(f(a(), x), a()) -> f(f(f(x, a()), f(a(), a())), a())}
   EDG:
    {(f#(f(a(), x), a()) -> f#(x, a()), f#(f(a(), x), a()) -> f#(a(), a()))
     (f#(f(a(), x), a()) -> f#(x, a()), f#(f(a(), x), a()) -> f#(f(f(x, a()), f(a(), a())), a()))
     (f#(f(a(), x), a()) -> f#(x, a()), f#(f(a(), x), a()) -> f#(f(x, a()), f(a(), a())))
     (f#(f(a(), x), a()) -> f#(x, a()), f#(f(a(), x), a()) -> f#(x, a()))
     (f#(f(a(), x), a()) -> f#(a(), a()), f#(f(a(), x), a()) -> f#(a(), a()))
     (f#(f(a(), x), a()) -> f#(a(), a()), f#(f(a(), x), a()) -> f#(f(f(x, a()), f(a(), a())), a()))
     (f#(f(a(), x), a()) -> f#(a(), a()), f#(f(a(), x), a()) -> f#(f(x, a()), f(a(), a())))
     (f#(f(a(), x), a()) -> f#(a(), a()), f#(f(a(), x), a()) -> f#(x, a()))
     (f#(f(a(), x), a()) -> f#(f(f(x, a()), f(a(), a())), a()), f#(f(a(), x), a()) -> f#(x, a()))
     (f#(f(a(), x), a()) -> f#(f(f(x, a()), f(a(), a())), a()), f#(f(a(), x), a()) -> f#(f(x, a()), f(a(), a())))
     (f#(f(a(), x), a()) -> f#(f(f(x, a()), f(a(), a())), a()), f#(f(a(), x), a()) -> f#(f(f(x, a()), f(a(), a())), a()))
     (f#(f(a(), x), a()) -> f#(f(f(x, a()), f(a(), a())), a()), f#(f(a(), x), a()) -> f#(a(), a()))
     (f#(f(a(), x), a()) -> f#(f(x, a()), f(a(), a())), f#(f(a(), x), a()) -> f#(x, a()))
     (f#(f(a(), x), a()) -> f#(f(x, a()), f(a(), a())), f#(f(a(), x), a()) -> f#(f(x, a()), f(a(), a())))
     (f#(f(a(), x), a()) -> f#(f(x, a()), f(a(), a())), f#(f(a(), x), a()) -> f#(f(f(x, a()), f(a(), a())), a()))
     (f#(f(a(), x), a()) -> f#(f(x, a()), f(a(), a())), f#(f(a(), x), a()) -> f#(a(), a()))}
    STATUS:
     arrows: 0.000000
     SCCS (1):
      Scc:
       {f#(f(a(), x), a()) -> f#(x, a()),
        f#(f(a(), x), a()) -> f#(f(x, a()), f(a(), a())),
        f#(f(a(), x), a()) -> f#(f(f(x, a()), f(a(), a())), a()),
        f#(f(a(), x), a()) -> f#(a(), a())}
      
      SCC (4):
       Strict:
        {f#(f(a(), x), a()) -> f#(x, a()),
         f#(f(a(), x), a()) -> f#(f(x, a()), f(a(), a())),
         f#(f(a(), x), a()) -> f#(f(f(x, a()), f(a(), a())), a()),
         f#(f(a(), x), a()) -> f#(a(), a())}
       Weak:
       {f(f(a(), x), a()) -> f(f(f(x, a()), f(a(), a())), a())}
       POLY:
        Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
        Interpretation:
         [f](x0, x1) = 0,
         
         [a] = 1,
         
         [f#](x0, x1) = x0
        Strict:
         f#(f(a(), x), a()) -> f#(a(), a())
         1 + 0x >= 1
         f#(f(a(), x), a()) -> f#(f(f(x, a()), f(a(), a())), a())
         1 + 0x >= 1 + 0x
         f#(f(a(), x), a()) -> f#(f(x, a()), f(a(), a()))
         1 + 0x >= 0 + 0x
         f#(f(a(), x), a()) -> f#(x, a())
         1 + 0x >= 1 + 0x
        Weak:
         f(f(a(), x), a()) -> f(f(f(x, a()), f(a(), a())), a())
         0 + 0x >= 0 + 0x
       SCCS (1):
        Scc:
         {f#(f(a(), x), a()) -> f#(x, a()),
          f#(f(a(), x), a()) -> f#(f(f(x, a()), f(a(), a())), a()),
          f#(f(a(), x), a()) -> f#(a(), a())}
        
        SCC (3):
         Strict:
          {f#(f(a(), x), a()) -> f#(x, a()),
           f#(f(a(), x), a()) -> f#(f(f(x, a()), f(a(), a())), a()),
           f#(f(a(), x), a()) -> f#(a(), a())}
         Weak:
         {f(f(a(), x), a()) -> f(f(f(x, a()), f(a(), a())), a())}
         Fail