YES
Time: 0.004329
TRS:
 {f 0() -> 1(),
  f s x -> g f x,
  f s x -> +(f x, s f x),
    g x -> +(x, s x)}
 DP:
  DP:
   {f# s x -> f# x,
    f# s x -> g# f x}
  TRS:
  {f 0() -> 1(),
   f s x -> g f x,
   f s x -> +(f x, s f x),
     g x -> +(x, s x)}
  UR:
   {  f 0() -> 1(),
      f s x -> g f x,
      f s x -> +(f x, s f x),
        g x -> +(x, s x),
    a(y, z) -> y,
    a(y, z) -> z}
   EDG:
    {(f# s x -> f# x, f# s x -> g# f x)
     (f# s x -> f# x, f# s x -> f# x)}
    STATUS:
     arrows: 0.500000
     SCCS (1):
      Scc:
       {f# s x -> f# x}
      
      SCC (1):
       Strict:
        {f# s x -> f# x}
       Weak:
       {f 0() -> 1(),
        f s x -> g f x,
        f s x -> +(f x, s f x),
          g x -> +(x, s x)}
       POLY:
        Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
        Interpretation:
         [+](x0, x1) = 0,
         
         [f](x0) = 0,
         
         [g](x0) = 0,
         
         [s](x0) = x0 + 1,
         
         [1] = 0,
         
         [0] = 0,
         
         [f#](x0) = x0
        Strict:
         f# s x -> f# x
         1 + 1x >= 0 + 1x
        Weak:
         g x -> +(x, s x)
         0 + 0x >= 0 + 0x
         f s x -> +(f x, s f x)
         0 + 0x >= 0 + 0x
         f s x -> g f x
         0 + 0x >= 0 + 0x
         f 0() -> 1()
         0 >= 0
       Qed