YES

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

Proof:
 DP Processor:
  DPs:
   f#(c(s(x),y)) -> f#(c(x,s(y)))
   g#(c(x,s(y))) -> g#(c(s(x),y))
  TRS:
   f(c(s(x),y)) -> f(c(x,s(y)))
   g(c(x,s(y))) -> g(c(s(x),y))
  Usable Rule Processor:
   DPs:
    f#(c(s(x),y)) -> f#(c(x,s(y)))
    g#(c(x,s(y))) -> g#(c(s(x),y))
   TRS:
    
   CDG Processor:
    DPs:
     f#(c(s(x),y)) -> f#(c(x,s(y)))
     g#(c(x,s(y))) -> g#(c(s(x),y))
    TRS:
     
    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)))
    Restore Modifier:
     DPs:
      f#(c(s(x),y)) -> f#(c(x,s(y)))
      g#(c(x,s(y))) -> g#(c(s(x),y))
     TRS:
      f(c(s(x),y)) -> f(c(x,s(y)))
      g(c(x,s(y))) -> g(c(s(x),y))
     SCC Processor:
      #sccs: 2
      #rules: 2
      #arcs: 2/4
      DPs:
       f#(c(s(x),y)) -> f#(c(x,s(y)))
      TRS:
       f(c(s(x),y)) -> f(c(x,s(y)))
       g(c(x,s(y))) -> g(c(s(x),y))
      Matrix Interpretation Processor:
       dimension: 1
       interpretation:
        [f#](x0) = x0,
        
        [g](x0) = 0,
        
        [f](x0) = 0,
        
        [c](x0, x1) = x0,
        
        [s](x0) = x0 + 1
       orientation:
        f#(c(s(x),y)) = x + 1 >= x = f#(c(x,s(y)))
        
        f(c(s(x),y)) = 0 >= 0 = f(c(x,s(y)))
        
        g(c(x,s(y))) = 0 >= 0 = g(c(s(x),y))
       problem:
        DPs:
         
        TRS:
         f(c(s(x),y)) -> f(c(x,s(y)))
         g(c(x,s(y))) -> g(c(s(x),y))
       Qed
      
      DPs:
       g#(c(x,s(y))) -> g#(c(s(x),y))
      TRS:
       f(c(s(x),y)) -> f(c(x,s(y)))
       g(c(x,s(y))) -> g(c(s(x),y))
      Matrix Interpretation Processor:
       dimension: 1
       interpretation:
        [g#](x0) = x0,
        
        [g](x0) = 1,
        
        [f](x0) = 0,
        
        [c](x0, x1) = x1,
        
        [s](x0) = x0 + 1
       orientation:
        g#(c(x,s(y))) = y + 1 >= y = g#(c(s(x),y))
        
        f(c(s(x),y)) = 0 >= 0 = f(c(x,s(y)))
        
        g(c(x,s(y))) = 1 >= 1 = g(c(s(x),y))
       problem:
        DPs:
         
        TRS:
         f(c(s(x),y)) -> f(c(x,s(y)))
         g(c(x,s(y))) -> g(c(s(x),y))
       Qed