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:
    
   ADG 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))
     f#(c(X,s(Y))) -> f#(c(s(X),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: 1
      #rules: 1
      #arcs: 2/4
      DPs:
       f#(c(X,s(Y))) -> f#(c(s(X),Y))
      TRS:
       f(c(X,s(Y))) -> f(c(s(X),Y))
       g(c(s(X),Y)) -> f(c(X,s(Y)))
      Matrix Interpretation Processor:
       dimension: 1
       interpretation:
        [f#](x0) = x0,
        
        [g](x0) = 0,
        
        [f](x0) = 0,
        
        [c](x0, x1) = x1,
        
        [s](x0) = x0 + 1
       orientation:
        f#(c(X,s(Y))) = Y + 1 >= Y = f#(c(s(X),Y))
        
        f(c(X,s(Y))) = 0 >= 0 = f(c(s(X),Y))
        
        g(c(s(X),Y)) = 0 >= 0 = f(c(X,s(Y)))
       problem:
        DPs:
         
        TRS:
         f(c(X,s(Y))) -> f(c(s(X),Y))
         g(c(s(X),Y)) -> f(c(X,s(Y)))
       Qed