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))))
  Restore Modifier:
   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))))
   SCC Processor:
    #sccs: 1
    #rules: 3
    #arcs: 9/9
    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))))
    Matrix Interpretation Processor:
     dimension: 1
     interpretation:
      [f#](x0, x1) = x1 + 1,
      
      [s](x0) = 1,
      
      [f](x0, x1) = 0,
      
      [c](x0) = x0 + 1
     orientation:
      f#(x,c(y)) = y + 2 >= y + 1 = f#(y,y)
      
      f#(x,c(y)) = y + 2 >= 2 = f#(x,s(f(y,y)))
      
      f#(s(x),s(y)) = 2 >= 2 = 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:
       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))))
     Matrix Interpretation Processor:
      dimension: 1
      interpretation:
       [f#](x0, x1) = x1,
       
       [s](x0) = 0,
       
       [f](x0, x1) = 0,
       
       [c](x0) = 1
      orientation:
       f#(x,c(y)) = 1 >= 0 = f#(x,s(f(y,y)))
       
       f#(s(x),s(y)) = 0 >= 0 = 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:
        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