YES

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

Proof:
 DP Processor:
  DPs:
   f#(x,c(y)) -> f#(y,y)
   f#(x,c(y)) -> f#(x,s(f(y,y)))
   f#(s(x),y) -> f#(x,s(c(y)))
  TRS:
   f(x,c(y)) -> f(x,s(f(y,y)))
   f(s(x),y) -> f(x,s(c(y)))
  EDG Processor:
   DPs:
    f#(x,c(y)) -> f#(y,y)
    f#(x,c(y)) -> f#(x,s(f(y,y)))
    f#(s(x),y) -> f#(x,s(c(y)))
   TRS:
    f(x,c(y)) -> f(x,s(f(y,y)))
    f(s(x),y) -> f(x,s(c(y)))
   graph:
    f#(s(x),y) -> f#(x,s(c(y))) -> f#(s(x),y) -> f#(x,s(c(y)))
    f#(x,c(y)) -> f#(y,y) -> f#(x,c(y)) -> f#(y,y)
    f#(x,c(y)) -> f#(y,y) -> f#(x,c(y)) -> f#(x,s(f(y,y)))
    f#(x,c(y)) -> f#(y,y) -> f#(s(x),y) -> f#(x,s(c(y)))
    f#(x,c(y)) -> f#(x,s(f(y,y))) -> f#(s(x),y) -> f#(x,s(c(y)))
   Restore Modifier:
    DPs:
     f#(x,c(y)) -> f#(y,y)
     f#(x,c(y)) -> f#(x,s(f(y,y)))
     f#(s(x),y) -> f#(x,s(c(y)))
    TRS:
     f(x,c(y)) -> f(x,s(f(y,y)))
     f(s(x),y) -> f(x,s(c(y)))
    SCC Processor:
     #sccs: 2
     #rules: 2
     #arcs: 5/9
     DPs:
      f#(x,c(y)) -> f#(y,y)
     TRS:
      f(x,c(y)) -> f(x,s(f(y,y)))
      f(s(x),y) -> f(x,s(c(y)))
     Matrix Interpretation Processor:
      dimension: 1
      interpretation:
       [f#](x0, x1) = x1 + 1,
       
       [s](x0) = 0,
       
       [f](x0, x1) = 0,
       
       [c](x0) = x0 + 1
      orientation:
       f#(x,c(y)) = y + 2 >= y + 1 = f#(y,y)
       
       f(x,c(y)) = 0 >= 0 = f(x,s(f(y,y)))
       
       f(s(x),y) = 0 >= 0 = f(x,s(c(y)))
      problem:
       DPs:
        
       TRS:
        f(x,c(y)) -> f(x,s(f(y,y)))
        f(s(x),y) -> f(x,s(c(y)))
      Qed
     
     DPs:
      f#(s(x),y) -> f#(x,s(c(y)))
     TRS:
      f(x,c(y)) -> f(x,s(f(y,y)))
      f(s(x),y) -> f(x,s(c(y)))
     Matrix Interpretation Processor:
      dimension: 1
      interpretation:
       [f#](x0, x1) = x0,
       
       [s](x0) = x0 + 1,
       
       [f](x0, x1) = x0,
       
       [c](x0) = 0
      orientation:
       f#(s(x),y) = x + 1 >= x = f#(x,s(c(y)))
       
       f(x,c(y)) = x >= x = f(x,s(f(y,y)))
       
       f(s(x),y) = x + 1 >= x = f(x,s(c(y)))
      problem:
       DPs:
        
       TRS:
        f(x,c(y)) -> f(x,s(f(y,y)))
        f(s(x),y) -> f(x,s(c(y)))
      Qed