YES
Time: 0.250396
TRS:
 {       g(x, y) -> x,
         g(x, y) -> y,
    f(x, y, s z) -> s f(0(), 1(), z),
  f(0(), 1(), x) -> f(s x, x, x)}
 DP:
  DP:
   {  f#(x, y, s z) -> f#(0(), 1(), z),
    f#(0(), 1(), x) -> f#(s x, x, x)}
  TRS:
  {       g(x, y) -> x,
          g(x, y) -> y,
     f(x, y, s z) -> s f(0(), 1(), z),
   f(0(), 1(), x) -> f(s x, x, x)}
  UR:
   {a(w, v) -> w,
    a(w, v) -> v}
   EDG:
    {(f#(x, y, s z) -> f#(0(), 1(), z), f#(0(), 1(), x) -> f#(s x, x, x))
     (f#(x, y, s z) -> f#(0(), 1(), z), f#(x, y, s z) -> f#(0(), 1(), z))
     (f#(0(), 1(), x) -> f#(s x, x, x), f#(x, y, s z) -> f#(0(), 1(), z))}
    STATUS:
     arrows: 0.250000
     SCCS (1):
      Scc:
       {  f#(x, y, s z) -> f#(0(), 1(), z),
        f#(0(), 1(), x) -> f#(s x, x, x)}
      
      SCC (2):
       Strict:
        {  f#(x, y, s z) -> f#(0(), 1(), z),
         f#(0(), 1(), x) -> f#(s x, x, x)}
       Weak:
       {       g(x, y) -> x,
               g(x, y) -> y,
          f(x, y, s z) -> s f(0(), 1(), z),
        f(0(), 1(), x) -> f(s x, x, x)}
       POLY:
        Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
        Interpretation:
         [f](x0, x1, x2) = x0 + x1 + 1,
         
         [g](x0, x1) = 0,
         
         [s](x0) = x0 + 1,
         
         [0] = 0,
         
         [1] = 1,
         
         [f#](x0, x1, x2) = x0
        Strict:
         f#(0(), 1(), x) -> f#(s x, x, x)
         0 + 1x >= 0 + 1x
         f#(x, y, s z) -> f#(0(), 1(), z)
         1 + 0x + 0y + 1z >= 0 + 1z
        Weak:
         f(0(), 1(), x) -> f(s x, x, x)
         2 + 1x >= 1 + 2x
         f(x, y, s z) -> s f(0(), 1(), z)
         2 + 0x + 1y + 1z >= 3 + 1z
         g(x, y) -> y
         0 + 0x + 0y >= 1y
         g(x, y) -> x
         0 + 0x + 0y >= 1x
       SCCS (0):