YES
Time: 0.004970
TRS:
 {f(a(), f(x, a())) -> f(a(), f(f(a(), x), f(a(), a())))}
 DP:
  DP:
   {f#(a(), f(x, a())) -> f#(f(a(), x), f(a(), a())),
    f#(a(), f(x, a())) -> f#(a(), x),
    f#(a(), f(x, a())) -> f#(a(), f(f(a(), x), f(a(), a()))),
    f#(a(), f(x, a())) -> f#(a(), a())}
  TRS:
  {f(a(), f(x, a())) -> f(a(), f(f(a(), x), f(a(), a())))}
  UR:
   {f(a(), f(x, a())) -> f(a(), f(f(a(), x), f(a(), a())))}
   EDG:
    {(f#(a(), f(x, a())) -> f#(a(), x), f#(a(), f(x, a())) -> f#(f(a(), x), f(a(), a())))
     (f#(a(), f(x, a())) -> f#(a(), x), f#(a(), f(x, a())) -> f#(a(), x))
     (f#(a(), f(x, a())) -> f#(a(), x), f#(a(), f(x, a())) -> f#(a(), f(f(a(), x), f(a(), a()))))
     (f#(a(), f(x, a())) -> f#(a(), x), f#(a(), f(x, a())) -> f#(a(), a()))}
    STATUS:
     arrows: 0.750000
     SCCS (1):
      Scc:
       {f#(a(), f(x, a())) -> f#(a(), x)}
      
      SCC (1):
       Strict:
        {f#(a(), f(x, a())) -> f#(a(), x)}
       Weak:
       {f(a(), f(x, a())) -> 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) = x0 + x1,
         
         [a] = 1,
         
         [f#](x0, x1) = x0 + x1
        Strict:
         f#(a(), f(x, a())) -> f#(a(), x)
         2 + 1x >= 1 + 1x
        Weak:
         f(a(), f(x, a())) -> f(a(), f(f(a(), x), f(a(), a())))
         2 + 1x >= 4 + 1x
       Qed