YES
Time: 0.014460
TRS:
 {f(0(), y) -> 0(),
  f(s x, y) -> f(f(x, y), y)}
 DP:
  DP:
   {f#(s x, y) -> f#(x, y),
    f#(s x, y) -> f#(f(x, y), y)}
  TRS:
  {f(0(), y) -> 0(),
   f(s x, y) -> f(f(x, y), y)}
  EDG:
   {(f#(s x, y) -> f#(x, y), f#(s x, y) -> f#(f(x, y), y))
    (f#(s x, y) -> f#(x, y), f#(s x, y) -> f#(x, y))
    (f#(s x, y) -> f#(f(x, y), y), f#(s x, y) -> f#(x, y))
    (f#(s x, y) -> f#(f(x, y), y), f#(s x, y) -> f#(f(x, y), y))}
   STATUS:
    arrows: 0.000000
    SCCS (1):
     Scc:
      {f#(s x, y) -> f#(x, y),
       f#(s x, y) -> f#(f(x, y), y)}
     
     SCC (2):
      Strict:
       {f#(s x, y) -> f#(x, y),
        f#(s x, y) -> f#(f(x, y), y)}
      Weak:
      {f(0(), y) -> 0(),
       f(s x, y) -> f(f(x, y), y)}
      POLY:
       Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
       Interpretation:
        [f](x0, x1) = 0,
        
        [s](x0) = x0 + 1,
        
        [0] = 0,
        
        [f#](x0, x1) = x0
       Strict:
        f#(s x, y) -> f#(f(x, y), y)
        1 + 0y + 1x >= 0 + 0y + 0x
        f#(s x, y) -> f#(x, y)
        1 + 0y + 1x >= 0 + 0y + 1x
       Weak:
        f(s x, y) -> f(f(x, y), y)
        0 + 0y + 0x >= 0 + 0y + 0x
        f(0(), y) -> 0()
        0 + 0y >= 0
      Qed