YES

Problem:
 f(x,c(y)) -> f(x,s(f(y,y)))
 f(s(x),s(y)) -> f(x,s(c(s(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),s(y)) -> f#(x,s(c(s(y))))
  TRS:
   f(x,c(y)) -> f(x,s(f(y,y)))
   f(s(x),s(y)) -> f(x,s(c(s(y))))
  CDG Processor:
   DPs:
    f#(x,c(y)) -> f#(y,y)
    f#(x,c(y)) -> f#(x,s(f(y,y)))
    f#(s(x),s(y)) -> f#(x,s(c(s(y))))
   TRS:
    f(x,c(y)) -> f(x,s(f(y,y)))
    f(s(x),s(y)) -> f(x,s(c(s(y))))
   graph:
    f#(s(x),s(y)) -> f#(x,s(c(s(y)))) -> f#(s(x),s(y)) -> f#(x,s(c(s(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),s(y)) -> f#(x,s(c(s(y))))
    f#(x,c(y)) -> f#(x,s(f(y,y))) -> f#(s(x),s(y)) -> f#(x,s(c(s(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),s(y)) -> f(x,s(c(s(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),s(y)) = 0 >= 0 = f(x,s(c(s(y))))
     problem:
      DPs:
       
      TRS:
       f(x,c(y)) -> f(x,s(f(y,y)))
       f(s(x),s(y)) -> f(x,s(c(s(y))))
     Qed
    
    DPs:
     f#(s(x),s(y)) -> f#(x,s(c(s(y))))
    TRS:
     f(x,c(y)) -> f(x,s(f(y,y)))
     f(s(x),s(y)) -> f(x,s(c(s(y))))
    Matrix Interpretation Processor:
     dimension: 1
     interpretation:
      [f#](x0, x1) = x0,
      
      [s](x0) = x0 + 1,
      
      [f](x0, x1) = 0,
      
      [c](x0) = x0
     orientation:
      f#(s(x),s(y)) = x + 1 >= x = f#(x,s(c(s(y))))
      
      f(x,c(y)) = 0 >= 0 = f(x,s(f(y,y)))
      
      f(s(x),s(y)) = 0 >= 0 = f(x,s(c(s(y))))
     problem:
      DPs:
       
      TRS:
       f(x,c(y)) -> f(x,s(f(y,y)))
       f(s(x),s(y)) -> f(x,s(c(s(y))))
     Qed