YES

Problem:
 f(g(x),s(0()),y) -> f(g(s(0())),y,g(x))
 g(s(x)) -> s(g(x))
 g(0()) -> 0()

Proof:
 DP Processor:
  DPs:
   f#(g(x),s(0()),y) -> g#(s(0()))
   f#(g(x),s(0()),y) -> f#(g(s(0())),y,g(x))
   g#(s(x)) -> g#(x)
  TRS:
   f(g(x),s(0()),y) -> f(g(s(0())),y,g(x))
   g(s(x)) -> s(g(x))
   g(0()) -> 0()
  CDG Processor:
   DPs:
    f#(g(x),s(0()),y) -> g#(s(0()))
    f#(g(x),s(0()),y) -> f#(g(s(0())),y,g(x))
    g#(s(x)) -> g#(x)
   TRS:
    f(g(x),s(0()),y) -> f(g(s(0())),y,g(x))
    g(s(x)) -> s(g(x))
    g(0()) -> 0()
   graph:
    f#(g(x),s(0()),y) -> g#(s(0())) -> g#(s(x)) -> g#(x)
   SCC Processor:
    #sccs: 0
    #rules: 0
    #arcs: 1/9