MAYBE
Time: 0.062341
TRS:
 {f(a(), f(a(), x)) -> f(a(), f(f(a(), x), f(a(), a())))}
 DP:
  DP:
   {f#(a(), f(a(), x)) -> f#(f(a(), x), f(a(), a())),
    f#(a(), f(a(), x)) -> f#(a(), f(f(a(), x), f(a(), a()))),
    f#(a(), f(a(), x)) -> f#(a(), a())}
  TRS:
  {f(a(), f(a(), x)) -> f(a(), f(f(a(), x), f(a(), a())))}
  UR:
   {f(a(), f(a(), x)) -> f(a(), f(f(a(), x), f(a(), a())))}
   EDG:
    {(f#(a(), f(a(), x)) -> f#(a(), a()), f#(a(), f(a(), x)) -> f#(a(), a()))
     (f#(a(), f(a(), x)) -> f#(a(), a()), f#(a(), f(a(), x)) -> f#(a(), f(f(a(), x), f(a(), a()))))
     (f#(a(), f(a(), x)) -> f#(a(), a()), f#(a(), f(a(), x)) -> f#(f(a(), x), f(a(), a())))
     (f#(a(), f(a(), x)) -> f#(f(a(), x), f(a(), a())), f#(a(), f(a(), x)) -> f#(f(a(), x), f(a(), a())))
     (f#(a(), f(a(), x)) -> f#(f(a(), x), f(a(), a())), f#(a(), f(a(), x)) -> f#(a(), f(f(a(), x), f(a(), a()))))
     (f#(a(), f(a(), x)) -> f#(f(a(), x), f(a(), a())), f#(a(), f(a(), x)) -> f#(a(), a()))
     (f#(a(), f(a(), x)) -> f#(a(), f(f(a(), x), f(a(), a()))), f#(a(), f(a(), x)) -> f#(f(a(), x), f(a(), a())))
     (f#(a(), f(a(), x)) -> f#(a(), f(f(a(), x), f(a(), a()))), f#(a(), f(a(), x)) -> f#(a(), f(f(a(), x), f(a(), a()))))
     (f#(a(), f(a(), x)) -> f#(a(), f(f(a(), x), f(a(), a()))), f#(a(), f(a(), x)) -> f#(a(), a()))}
    STATUS:
     arrows: 0.000000
     SCCS (1):
      Scc:
       {f#(a(), f(a(), x)) -> f#(f(a(), x), f(a(), a())),
        f#(a(), f(a(), x)) -> f#(a(), f(f(a(), x), f(a(), a()))),
        f#(a(), f(a(), x)) -> f#(a(), a())}
      
      SCC (3):
       Strict:
        {f#(a(), f(a(), x)) -> f#(f(a(), x), f(a(), a())),
         f#(a(), f(a(), x)) -> f#(a(), f(f(a(), x), f(a(), a()))),
         f#(a(), f(a(), x)) -> f#(a(), a())}
       Weak:
       {f(a(), f(a(), x)) -> f(a(), f(f(a(), x), f(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 + 1
        Strict:
         f#(a(), f(a(), x)) -> f#(a(), a())
         2 + 0x >= 2
         f#(a(), f(a(), x)) -> f#(a(), f(f(a(), x), f(a(), a())))
         2 + 0x >= 2 + 0x
         f#(a(), f(a(), x)) -> f#(f(a(), x), f(a(), a()))
         2 + 0x >= 1 + 0x
        Weak:
         f(a(), f(a(), x)) -> f(a(), f(f(a(), x), f(a(), a())))
         0 + 0x >= 0 + 0x
       SCCS (1):
        Scc:
         {f#(a(), f(a(), x)) -> f#(a(), f(f(a(), x), f(a(), a()))),
          f#(a(), f(a(), x)) -> f#(a(), a())}
        
        SCC (2):
         Strict:
          {f#(a(), f(a(), x)) -> f#(a(), f(f(a(), x), f(a(), a()))),
           f#(a(), f(a(), x)) -> f#(a(), a())}
         Weak:
         {f(a(), f(a(), x)) -> f(a(), f(f(a(), x), f(a(), a())))}
         POLY:
          Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
          Interpretation:
           [f](x0, x1) = 1,
           
           [a] = 0,
           
           [f#](x0, x1) = x0
          Strict:
           f#(a(), f(a(), x)) -> f#(a(), a())
           1 + 0x >= 0
           f#(a(), f(a(), x)) -> f#(a(), f(f(a(), x), f(a(), a())))
           1 + 0x >= 1 + 0x
          Weak:
           f(a(), f(a(), x)) -> f(a(), f(f(a(), x), f(a(), a())))
           1 + 0x >= 1 + 0x
         SCCS (1):
          Scc:
           {f#(a(), f(a(), x)) -> f#(a(), f(f(a(), x), f(a(), a())))}
          
          SCC (1):
           Strict:
            {f#(a(), f(a(), x)) -> f#(a(), f(f(a(), x), f(a(), a())))}
           Weak:
           {f(a(), f(a(), x)) -> f(a(), f(f(a(), x), f(a(), a())))}
           Fail