YES
Time: 0.003367
TRS:
 {f(g x, s 0(), y) -> f(y, y, g x),
             g s x -> s g x,
             g 0() -> 0()}
 DP:
  DP:
   {f#(g x, s 0(), y) -> f#(y, y, g x),
               g# s x -> g# x}
  TRS:
  {f(g x, s 0(), y) -> f(y, y, g x),
              g s x -> s g x,
              g 0() -> 0()}
  UR:
   {g s x -> s g x,
    g 0() -> 0()}
   EDG:
    {(g# s x -> g# x, g# s x -> g# x)}
    STATUS:
     arrows: 0.750000
     SCCS (1):
      Scc:
       {g# s x -> g# x}
      
      
      SCC (1):
       Strict:
        {g# s x -> g# x}
       Weak:
       {f(g x, s 0(), y) -> f(y, y, g x),
                   g s x -> s g x,
                   g 0() -> 0()}
       POLY:
        Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
        Interpretation:
         [f](x0, x1, x2) = x0,
         
         [g](x0) = 1,
         
         [s](x0) = x0 + 1,
         
         [0] = 1,
         
         [g#](x0) = x0
        Strict:
         g# s x -> g# x
         1 + 1x >= 0 + 1x
        Weak:
         g 0() -> 0()
         1 >= 1
         g s x -> s g x
         1 + 0x >= 2 + 0x
         f(g x, s 0(), y) -> f(y, y, g x)
         0 + 1y + 0x >= 1 + 0y + 0x
       Qed