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))
  CDG 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))
   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)))
   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