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))
  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)))
    g(c(x,s(y))) -> g(c(s(x),y))
    g(s(f(x))) -> g(f(x))
   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)))
   SCC Processor:
    #sccs: 2
    #rules: 3
    #arcs: 5/9
    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))
     g(s(f(x))) -> g(f(x))
    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))
      
      g(s(f(x))) = 0 >= 0 = g(f(x))
     problem:
      DPs:
       
      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))
     Qed
    
    DPs:
     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))
    Matrix Interpretation Processor:
     dimension: 1
     interpretation:
      [g#](x0) = x0,
      
      [g](x0) = 0,
      
      [f](x0) = 0,
      
      [c](x0, x1) = 0,
      
      [s](x0) = 1
     orientation:
      g#(c(x,s(y))) = 0 >= 0 = g#(c(s(x),y))
      
      g#(s(f(x))) = 1 >= 0 = g#(f(x))
      
      f(c(s(x),y)) = 0 >= 0 = f(c(x,s(y)))
      
      g(c(x,s(y))) = 0 >= 0 = g(c(s(x),y))
      
      g(s(f(x))) = 0 >= 0 = g(f(x))
     problem:
      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))
       g(s(f(x))) -> g(f(x))
     Matrix Interpretation Processor:
      dimension: 1
      interpretation:
       [g#](x0) = x0,
       
       [g](x0) = 0,
       
       [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))) = 0 >= 0 = g(c(s(x),y))
       
       g(s(f(x))) = 0 >= 0 = g(f(x))
      problem:
       DPs:
        
       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))
      Qed