MAYBE
Time: 0.067251
TRS:
 {f(a(), f(a(), x)) -> f(a(), f(f(a(), a()), f(a(), x)))}
 DP:
  DP:
   {f#(a(), f(a(), x)) -> f#(f(a(), a()), f(a(), x)),
    f#(a(), f(a(), x)) -> f#(a(), f(f(a(), a()), f(a(), x))),
    f#(a(), f(a(), x)) -> f#(a(), a())}
  TRS:
  {f(a(), f(a(), x)) -> f(a(), f(f(a(), a()), f(a(), x)))}
  UR:
   {f(a(), f(a(), x)) -> f(a(), f(f(a(), a()), f(a(), x)))}
   EDG:
    {(f#(a(), f(a(), x)) -> f#(f(a(), a()), f(a(), x)), f#(a(), f(a(), x)) -> f#(a(), a()))
     (f#(a(), f(a(), x)) -> f#(f(a(), a()), f(a(), x)), f#(a(), f(a(), x)) -> f#(a(), f(f(a(), a()), f(a(), x))))
     (f#(a(), f(a(), x)) -> f#(f(a(), a()), f(a(), x)), f#(a(), f(a(), x)) -> f#(f(a(), a()), f(a(), x)))
     (f#(a(), f(a(), x)) -> f#(a(), a()), f#(a(), f(a(), x)) -> f#(f(a(), a()), f(a(), x)))
     (f#(a(), f(a(), x)) -> f#(a(), a()), f#(a(), f(a(), x)) -> f#(a(), f(f(a(), a()), f(a(), x))))
     (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(), a()), f(a(), x))), f#(a(), f(a(), x)) -> f#(f(a(), a()), f(a(), x)))
     (f#(a(), f(a(), x)) -> f#(a(), f(f(a(), a()), f(a(), x))), f#(a(), f(a(), x)) -> f#(a(), f(f(a(), a()), f(a(), x))))
     (f#(a(), f(a(), x)) -> f#(a(), f(f(a(), a()), f(a(), x))), f#(a(), f(a(), x)) -> f#(a(), a()))}
    STATUS:
     arrows: 0.000000
     SCCS (1):
      Scc:
       {f#(a(), f(a(), x)) -> f#(f(a(), a()), f(a(), x)),
        f#(a(), f(a(), x)) -> f#(a(), f(f(a(), a()), f(a(), x))),
        f#(a(), f(a(), x)) -> f#(a(), a())}
      
      SCC (3):
       Strict:
        {f#(a(), f(a(), x)) -> f#(f(a(), a()), f(a(), x)),
         f#(a(), f(a(), x)) -> f#(a(), f(f(a(), a()), f(a(), x))),
         f#(a(), f(a(), x)) -> f#(a(), a())}
       Weak:
       {f(a(), f(a(), x)) -> f(a(), f(f(a(), a()), f(a(), x)))}
       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#(a(), f(a(), x)) -> f#(a(), a())
         1 + 0x >= 1
         f#(a(), f(a(), x)) -> f#(a(), f(f(a(), a()), f(a(), x)))
         1 + 0x >= 1 + 0x
         f#(a(), f(a(), x)) -> f#(f(a(), a()), f(a(), x))
         1 + 0x >= 0 + 0x
        Weak:
         f(a(), f(a(), x)) -> f(a(), f(f(a(), a()), f(a(), x)))
         0 + 0x >= 0 + 0x
       SCCS (1):
        Scc:
         {f#(a(), f(a(), x)) -> f#(a(), f(f(a(), a()), f(a(), x))),
          f#(a(), f(a(), x)) -> f#(a(), a())}
        
        SCC (2):
         Strict:
          {f#(a(), f(a(), x)) -> f#(a(), f(f(a(), a()), f(a(), x))),
           f#(a(), f(a(), x)) -> f#(a(), a())}
         Weak:
         {f(a(), f(a(), x)) -> f(a(), f(f(a(), a()), f(a(), x)))}
         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(), a()), f(a(), x)))
           1 + 0x >= 1 + 0x
          Weak:
           f(a(), f(a(), x)) -> f(a(), f(f(a(), a()), f(a(), x)))
           1 + 0x >= 1 + 0x
         SCCS (1):
          Scc:
           {f#(a(), f(a(), x)) -> f#(a(), f(f(a(), a()), f(a(), x)))}
          
          SCC (1):
           Strict:
            {f#(a(), f(a(), x)) -> f#(a(), f(f(a(), a()), f(a(), x)))}
           Weak:
           {f(a(), f(a(), x)) -> f(a(), f(f(a(), a()), f(a(), x)))}
           Fail