YES
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:
  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)}
  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))}
   SCCS:
    Scc:
     { f#(x, y, s(z)) -> f#(0(), 1(), z),
      f#(0(), 1(), x) -> f#(s(x), x, x)}
    SCC:
     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)}
     SPSC:
      Simple Projection:
       pi(f#) = 2
      Strict:
       {f#(0(), 1(), x) -> f#(s(x), x, x)}
      EDG:
       {}
       SCCS:
        
        Qed