YES

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

Proof:
 DP Processor:
  DPs:
   f#(s(x)) -> g#(s(s(x)))
   g#(s(s(x))) -> f#(x)
  TRS:
   f(0()) -> s(0())
   f(s(x)) -> g(s(s(x)))
   g(0()) -> s(0())
   g(s(0())) -> s(0())
   g(s(s(x))) -> f(x)
  TDG Processor:
   DPs:
    f#(s(x)) -> g#(s(s(x)))
    g#(s(s(x))) -> f#(x)
   TRS:
    f(0()) -> s(0())
    f(s(x)) -> g(s(s(x)))
    g(0()) -> s(0())
    g(s(0())) -> s(0())
    g(s(s(x))) -> f(x)
   graph:
    g#(s(s(x))) -> f#(x) -> f#(s(x)) -> g#(s(s(x)))
    f#(s(x)) -> g#(s(s(x))) -> g#(s(s(x))) -> f#(x)
   CDG Processor:
    DPs:
     f#(s(x)) -> g#(s(s(x)))
     g#(s(s(x))) -> f#(x)
    TRS:
     f(0()) -> s(0())
     f(s(x)) -> g(s(s(x)))
     g(0()) -> s(0())
     g(s(0())) -> s(0())
     g(s(s(x))) -> f(x)
    graph:
     f#(s(x)) -> g#(s(s(x))) -> g#(s(s(x))) -> f#(x)
    SCC Processor:
     #sccs: 0
     #rules: 0
     #arcs: 1/4