YES

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

Proof:
 DP Processor:
  DPs:
   f#(c(s(x),y)) -> f#(c(x,s(y)))
   f#(c(s(x),s(y))) -> g#(c(x,y))
   g#(c(x,s(y))) -> g#(c(s(x),y))
   g#(c(s(x),s(y))) -> f#(c(x,y))
  TRS:
   f(c(s(x),y)) -> f(c(x,s(y)))
   f(c(s(x),s(y))) -> g(c(x,y))
   g(c(x,s(y))) -> g(c(s(x),y))
   g(c(s(x),s(y))) -> f(c(x,y))
  TDG Processor:
   DPs:
    f#(c(s(x),y)) -> f#(c(x,s(y)))
    f#(c(s(x),s(y))) -> g#(c(x,y))
    g#(c(x,s(y))) -> g#(c(s(x),y))
    g#(c(s(x),s(y))) -> f#(c(x,y))
   TRS:
    f(c(s(x),y)) -> f(c(x,s(y)))
    f(c(s(x),s(y))) -> g(c(x,y))
    g(c(x,s(y))) -> g(c(s(x),y))
    g(c(s(x),s(y))) -> f(c(x,y))
   graph:
    g#(c(s(x),s(y))) -> f#(c(x,y)) -> f#(c(s(x),s(y))) -> g#(c(x,y))
    g#(c(s(x),s(y))) -> f#(c(x,y)) -> f#(c(s(x),y)) -> f#(c(x,s(y)))
    g#(c(x,s(y))) -> g#(c(s(x),y)) -> g#(c(s(x),s(y))) -> f#(c(x,y))
    g#(c(x,s(y))) -> g#(c(s(x),y)) -> g#(c(x,s(y))) -> g#(c(s(x),y))
    f#(c(s(x),s(y))) -> g#(c(x,y)) -> g#(c(s(x),s(y))) -> f#(c(x,y))
    f#(c(s(x),s(y))) -> g#(c(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),s(y))) -> g#(c(x,y))
    f#(c(s(x),y)) -> f#(c(x,s(y))) -> f#(c(s(x),y)) -> f#(c(x,s(y)))
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [g#](x0) = 2x0 + 1/2,
     
     [f#](x0) = 2x0,
     
     [g](x0) = 0,
     
     [f](x0) = 0,
     
     [c](x0, x1) = 2x0 + 2x1,
     
     [s](x0) = x0 + 1
    orientation:
     f#(c(s(x),y)) = 4x + 4y + 4 >= 4x + 4y + 4 = f#(c(x,s(y)))
     
     f#(c(s(x),s(y))) = 4x + 4y + 8 >= 4x + 4y + 1/2 = g#(c(x,y))
     
     g#(c(x,s(y))) = 4x + 4y + 9/2 >= 4x + 4y + 9/2 = g#(c(s(x),y))
     
     g#(c(s(x),s(y))) = 4x + 4y + 17/2 >= 4x + 4y = f#(c(x,y))
     
     f(c(s(x),y)) = 0 >= 0 = f(c(x,s(y)))
     
     f(c(s(x),s(y))) = 0 >= 0 = g(c(x,y))
     
     g(c(x,s(y))) = 0 >= 0 = g(c(s(x),y))
     
     g(c(s(x),s(y))) = 0 >= 0 = f(c(x,y))
    problem:
     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)))
      f(c(s(x),s(y))) -> g(c(x,y))
      g(c(x,s(y))) -> g(c(s(x),y))
      g(c(s(x),s(y))) -> f(c(x,y))
    SCC Processor:
     #sccs: 2
     #rules: 2
     #arcs: 8/4
     DPs:
      f#(c(s(x),y)) -> f#(c(x,s(y)))
     TRS:
      f(c(s(x),y)) -> f(c(x,s(y)))
      f(c(s(x),s(y))) -> g(c(x,y))
      g(c(x,s(y))) -> g(c(s(x),y))
      g(c(s(x),s(y))) -> f(c(x,y))
     Arctic Interpretation Processor:
      dimension: 1
      interpretation:
       [f#](x0) = x0,
       
       [g](x0) = 1,
       
       [f](x0) = 1,
       
       [c](x0, x1) = x0,
       
       [s](x0) = 1x0
      orientation:
       f#(c(s(x),y)) = 1x >= x = f#(c(x,s(y)))
       
       f(c(s(x),y)) = 1 >= 1 = f(c(x,s(y)))
       
       f(c(s(x),s(y))) = 1 >= 1 = g(c(x,y))
       
       g(c(x,s(y))) = 1 >= 1 = g(c(s(x),y))
       
       g(c(s(x),s(y))) = 1 >= 1 = f(c(x,y))
      problem:
       DPs:
        
       TRS:
        f(c(s(x),y)) -> f(c(x,s(y)))
        f(c(s(x),s(y))) -> g(c(x,y))
        g(c(x,s(y))) -> g(c(s(x),y))
        g(c(s(x),s(y))) -> f(c(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)))
      f(c(s(x),s(y))) -> g(c(x,y))
      g(c(x,s(y))) -> g(c(s(x),y))
      g(c(s(x),s(y))) -> f(c(x,y))
     Arctic Interpretation Processor:
      dimension: 1
      interpretation:
       [g#](x0) = x0 + 0,
       
       [g](x0) = 4,
       
       [f](x0) = 4,
       
       [c](x0, x1) = x1 + 0,
       
       [s](x0) = 3x0 + 4
      orientation:
       g#(c(x,s(y))) = 3y + 4 >= y + 0 = g#(c(s(x),y))
       
       f(c(s(x),y)) = 4 >= 4 = f(c(x,s(y)))
       
       f(c(s(x),s(y))) = 4 >= 4 = g(c(x,y))
       
       g(c(x,s(y))) = 4 >= 4 = g(c(s(x),y))
       
       g(c(s(x),s(y))) = 4 >= 4 = f(c(x,y))
      problem:
       DPs:
        
       TRS:
        f(c(s(x),y)) -> f(c(x,s(y)))
        f(c(s(x),s(y))) -> g(c(x,y))
        g(c(x,s(y))) -> g(c(s(x),y))
        g(c(s(x),s(y))) -> f(c(x,y))
      Qed