YES

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

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