YES
Time: 0.064043
TRS:
 {  f(x, 0()) -> s 0(),
  f(s x, s y) -> s f(x, y),
    g(0(), x) -> g(f(x, x), x)}
 DP:
  DP:
   {f#(s x, s y) -> f#(x, y),
      g#(0(), x) -> f#(x, x),
      g#(0(), x) -> g#(f(x, x), x)}
  TRS:
  {  f(x, 0()) -> s 0(),
   f(s x, s y) -> s f(x, y),
     g(0(), x) -> g(f(x, x), x)}
  UR:
   {  f(x, 0()) -> s 0(),
    f(s x, s y) -> s f(x, y),
        a(z, w) -> z,
        a(z, w) -> w}
   EDG:
    {(g#(0(), x) -> f#(x, x), f#(s x, s y) -> f#(x, y))
     (f#(s x, s y) -> f#(x, y), f#(s x, s y) -> f#(x, y))}
    STATUS:
     arrows: 0.777778
     SCCS (1):
      Scc:
       {f#(s x, s y) -> f#(x, y)}
      
      
      
      SCC (1):
       Strict:
        {f#(s x, s y) -> f#(x, y)}
       Weak:
       {  f(x, 0()) -> s 0(),
        f(s x, s y) -> s f(x, y),
          g(0(), x) -> g(f(x, x), x)}
       POLY:
        Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
        Interpretation:
         [f](x0, x1) = x0 + 1,
         
         [g](x0, x1) = x0 + x1 + 1,
         
         [s](x0) = x0 + 1,
         
         [0] = 1,
         
         [f#](x0, x1) = x0
        Strict:
         f#(s x, s y) -> f#(x, y)
         1 + 0x + 1y >= 0 + 0x + 1y
        Weak:
         g(0(), x) -> g(f(x, x), x)
         2 + 1x >= 2 + 2x
         f(s x, s y) -> s f(x, y)
         2 + 0x + 1y >= 2 + 0x + 1y
         f(x, 0()) -> s 0()
         2 + 0x >= 2
       Qed