YES

Problem:
 f(c(X,s(Y))) -> f(c(s(X),Y))
 g(c(s(X),Y)) -> f(c(X,s(Y)))

Proof:
 DP Processor:
  DPs:
   f#(c(X,s(Y))) -> f#(c(s(X),Y))
   g#(c(s(X),Y)) -> f#(c(X,s(Y)))
  TRS:
   f(c(X,s(Y))) -> f(c(s(X),Y))
   g(c(s(X),Y)) -> f(c(X,s(Y)))
  Usable Rule Processor:
   DPs:
    f#(c(X,s(Y))) -> f#(c(s(X),Y))
    g#(c(s(X),Y)) -> f#(c(X,s(Y)))
   TRS:
    
   CDG Processor:
    DPs:
     f#(c(X,s(Y))) -> f#(c(s(X),Y))
     g#(c(s(X),Y)) -> f#(c(X,s(Y)))
    TRS:
     
    graph:
     g#(c(s(X),Y)) -> f#(c(X,s(Y))) -> f#(c(X,s(Y))) -> f#(c(s(X),Y))
    Restore Modifier:
     DPs:
      f#(c(X,s(Y))) -> f#(c(s(X),Y))
      g#(c(s(X),Y)) -> f#(c(X,s(Y)))
     TRS:
      f(c(X,s(Y))) -> f(c(s(X),Y))
      g(c(s(X),Y)) -> f(c(X,s(Y)))
     SCC Processor:
      #sccs: 0
      #rules: 0
      #arcs: 1/4