YES
Time: 0.017666
TRS:
 {f(a(), a()) -> f(a(), b()),
  f(a(), b()) -> f(s a(), c()),
  f(s X, c()) -> f(X, c()),
  f(c(), c()) -> f(a(), a())}
 DP:
  DP:
   {f#(a(), a()) -> f#(a(), b()),
    f#(a(), b()) -> f#(s a(), c()),
    f#(s X, c()) -> f#(X, c()),
    f#(c(), c()) -> f#(a(), a())}
  TRS:
  {f(a(), a()) -> f(a(), b()),
   f(a(), b()) -> f(s a(), c()),
   f(s X, c()) -> f(X, c()),
   f(c(), c()) -> f(a(), a())}
  UR:
   {}
   EDG:
    {(f#(a(), b()) -> f#(s a(), c()), f#(s X, c()) -> f#(X, c()))
     (f#(c(), c()) -> f#(a(), a()), f#(a(), a()) -> f#(a(), b()))
     (f#(s X, c()) -> f#(X, c()), f#(s X, c()) -> f#(X, c()))
     (f#(s X, c()) -> f#(X, c()), f#(c(), c()) -> f#(a(), a()))
     (f#(a(), a()) -> f#(a(), b()), f#(a(), b()) -> f#(s a(), c()))}
    STATUS:
     arrows: 0.687500
     SCCS (1):
      Scc:
       {f#(a(), a()) -> f#(a(), b()),
        f#(a(), b()) -> f#(s a(), c()),
        f#(s X, c()) -> f#(X, c()),
        f#(c(), c()) -> f#(a(), a())}
      
      SCC (4):
       Strict:
        {f#(a(), a()) -> f#(a(), b()),
         f#(a(), b()) -> f#(s a(), c()),
         f#(s X, c()) -> f#(X, c()),
         f#(c(), c()) -> f#(a(), a())}
       Weak:
       {f(a(), a()) -> f(a(), b()),
        f(a(), b()) -> f(s a(), c()),
        f(s X, c()) -> f(X, c()),
        f(c(), c()) -> f(a(), a())}
       POLY:
        Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
        Interpretation:
         [f](x0, x1) = x0 + x1,
         
         [s](x0) = x0,
         
         [a] = 0,
         
         [b] = 0,
         
         [c] = 1,
         
         [f#](x0, x1) = x0
        Strict:
         f#(c(), c()) -> f#(a(), a())
         1 >= 0
         f#(s X, c()) -> f#(X, c())
         0 + 1X >= 0 + 1X
         f#(a(), b()) -> f#(s a(), c())
         0 >= 0
         f#(a(), a()) -> f#(a(), b())
         0 >= 0
        Weak:
         f(c(), c()) -> f(a(), a())
         2 >= 0
         f(s X, c()) -> f(X, c())
         1 + 1X >= 1 + 1X
         f(a(), b()) -> f(s a(), c())
         0 >= 1
         f(a(), a()) -> f(a(), b())
         0 >= 0
       SCCS (1):
        Scc:
         {f#(s X, c()) -> f#(X, c())}
        
        
        
        SCC (1):
         Strict:
          {f#(s X, c()) -> f#(X, c())}
         Weak:
         {f(a(), a()) -> f(a(), b()),
          f(a(), b()) -> f(s a(), c()),
          f(s X, c()) -> f(X, c()),
          f(c(), c()) -> f(a(), a())}
         POLY:
          Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
          Interpretation:
           [f](x0, x1) = x0 + 1,
           
           [s](x0) = x0 + 1,
           
           [a] = 1,
           
           [b] = 0,
           
           [c] = 1,
           
           [f#](x0, x1) = x0 + x1
          Strict:
           f#(s X, c()) -> f#(X, c())
           2 + 1X >= 1 + 1X
          Weak:
           f(c(), c()) -> f(a(), a())
           2 >= 2
           f(s X, c()) -> f(X, c())
           2 + 1X >= 1 + 1X
           f(a(), b()) -> f(s a(), c())
           2 >= 3
           f(a(), a()) -> f(a(), b())
           2 >= 2
         Qed