YES
Time: 0.009452
TRS:
 {f(f(a(), x), a()) -> f(f(f(a(), a()), f(x, a())), a())}
 DP:
  DP:
   {f#(f(a(), x), a()) -> f#(x, a()),
    f#(f(a(), x), a()) -> f#(f(f(a(), a()), f(x, a())), a()),
    f#(f(a(), x), a()) -> f#(f(a(), a()), f(x, a())),
    f#(f(a(), x), a()) -> f#(a(), a())}
  TRS:
  {f(f(a(), x), a()) -> f(f(f(a(), a()), f(x, a())), a())}
  UR:
   {f(f(a(), x), a()) -> f(f(f(a(), a()), f(x, 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(a(), a()), f(x, a())))
     (f#(f(a(), x), a()) -> f#(x, a()), f#(f(a(), x), a()) -> f#(f(f(a(), a()), f(x, a())), a()))
     (f#(f(a(), x), a()) -> f#(x, a()), f#(f(a(), x), a()) -> f#(x, a()))}
    STATUS:
     arrows: 0.750000
     SCCS (1):
      Scc:
       {f#(f(a(), x), a()) -> f#(x, a())}
      
      SCC (1):
       Strict:
        {f#(f(a(), x), a()) -> f#(x, a())}
       Weak:
       {f(f(a(), x), a()) -> f(f(f(a(), a()), f(x, 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#(f(a(), x), a()) -> f#(x, a())
         2 + 1x >= 1 + 1x
        Weak:
         f(f(a(), x), a()) -> f(f(f(a(), a()), f(x, a())), a())
         2 + 1x >= 4 + 1x
       Qed