YES
Time: 0.008684
TRS:
 {  f(x, c y) -> f(x, s f(y, y)),
  f(s x, s y) -> f(x, s c s y)}
 DP:
  DP:
   {  f#(x, c y) -> f#(x, s f(y, y)),
      f#(x, c y) -> f#(y, y),
    f#(s x, s y) -> f#(x, s c s y)}
  TRS:
  {  f(x, c y) -> f(x, s f(y, y)),
   f(s x, s y) -> f(x, s c s y)}
  UR:
   {  f(x, c y) -> f(x, s f(y, y)),
    f(s x, s y) -> f(x, s c s y)}
   EDG:
    {(f#(x, c y) -> f#(y, y), f#(s x, s y) -> f#(x, s c s y))
     (f#(x, c y) -> f#(y, y), f#(x, c y) -> f#(y, y))
     (f#(x, c y) -> f#(y, y), f#(x, c y) -> f#(x, s f(y, y)))
     (f#(s x, s y) -> f#(x, s c s y), f#(s x, s y) -> f#(x, s c s y))
     (f#(x, c y) -> f#(x, s f(y, y)), f#(s x, s y) -> f#(x, s c s y))}
    STATUS:
     arrows: 0.444444
     SCCS (2):
      Scc:
       {f#(x, c y) -> f#(y, y)}
      Scc:
       {f#(s x, s y) -> f#(x, s c s y)}
      
      SCC (1):
       Strict:
        {f#(x, c y) -> f#(y, y)}
       Weak:
       {  f(x, c y) -> f(x, s f(y, y)),
        f(s x, s y) -> f(x, s c s y)}
       POLY:
        Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
        Interpretation:
         [f](x0, x1) = 0,
         
         [s](x0) = 1,
         
         [c](x0) = x0 + 1,
         
         [f#](x0, x1) = x0 + 1
        Strict:
         f#(x, c y) -> f#(y, y)
         2 + 0x + 1y >= 1 + 1y
        Weak:
         f(s x, s y) -> f(x, s c s y)
         0 + 0x + 0y >= 0 + 0x + 0y
         f(x, c y) -> f(x, s f(y, y))
         0 + 0x + 0y >= 0 + 0x + 0y
       Qed
     
     SCC (1):
      Strict:
       {f#(s x, s y) -> f#(x, s c s y)}
      Weak:
      {  f(x, c y) -> f(x, s f(y, y)),
       f(s x, s y) -> f(x, s c s y)}
      POLY:
       Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
       Interpretation:
        [f](x0, x1) = 0,
        
        [s](x0) = x0 + 1,
        
        [c](x0) = x0,
        
        [f#](x0, x1) = x0 + 1
       Strict:
        f#(s x, s y) -> f#(x, s c s y)
        2 + 1x + 0y >= 1 + 1x + 0y
       Weak:
        f(s x, s y) -> f(x, s c s y)
        0 + 0x + 0y >= 0 + 0x + 0y
        f(x, c y) -> f(x, s f(y, y))
        0 + 0x + 0y >= 0 + 0x + 0y
      Qed