YES

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

Proof:
 DP Processor:
  DPs:
   f#(c(s(x),y)) -> f#(c(x,s(y)))
   g#(c(x,s(y))) -> g#(c(s(x),y))
   g#(s(f(x))) -> g#(f(x))
  TRS:
   f(c(s(x),y)) -> f(c(x,s(y)))
   g(c(x,s(y))) -> g(c(s(x),y))
   g(s(f(x))) -> g(f(x))
  Usable Rule Processor:
   DPs:
    f#(c(s(x),y)) -> f#(c(x,s(y)))
    g#(c(x,s(y))) -> g#(c(s(x),y))
    g#(s(f(x))) -> g#(f(x))
   TRS:
    f(c(s(x),y)) -> f(c(x,s(y)))
   TDG Processor:
    DPs:
     f#(c(s(x),y)) -> f#(c(x,s(y)))
     g#(c(x,s(y))) -> g#(c(s(x),y))
     g#(s(f(x))) -> g#(f(x))
    TRS:
     f(c(s(x),y)) -> f(c(x,s(y)))
    graph:
     g#(c(x,s(y))) -> g#(c(s(x),y)) -> g#(s(f(x))) -> g#(f(x))
     g#(c(x,s(y))) -> g#(c(s(x),y)) -> g#(c(x,s(y))) -> g#(c(s(x),y))
     g#(s(f(x))) -> g#(f(x)) -> g#(s(f(x))) -> g#(f(x))
     g#(s(f(x))) -> g#(f(x)) -> g#(c(x,s(y))) -> g#(c(s(x),y))
     f#(c(s(x),y)) -> f#(c(x,s(y))) -> f#(c(s(x),y)) -> f#(c(x,s(y)))
    EDG Processor:
     DPs:
      f#(c(s(x),y)) -> f#(c(x,s(y)))
      g#(c(x,s(y))) -> g#(c(s(x),y))
      g#(s(f(x))) -> g#(f(x))
     TRS:
      f(c(s(x),y)) -> f(c(x,s(y)))
     graph:
      g#(c(x,s(y))) -> g#(c(s(x),y)) ->
      g#(c(x,s(y))) -> g#(c(s(x),y))
      f#(c(s(x),y)) -> f#(c(x,s(y))) -> f#(c(s(x),y)) -> f#(c(x,s(y)))
     CDG Processor:
      DPs:
       f#(c(s(x),y)) -> f#(c(x,s(y)))
       g#(c(x,s(y))) -> g#(c(s(x),y))
       g#(s(f(x))) -> g#(f(x))
      TRS:
       f(c(s(x),y)) -> f(c(x,s(y)))
      graph:
       
      Qed