YES

Problem:
 f(s(x),y) -> f(x,f(x,y))
 f(0(),y) -> c(y,y)

Proof:
 DP Processor:
  DPs:
   f#(s(x),y) -> f#(x,y)
   f#(s(x),y) -> f#(x,f(x,y))
  TRS:
   f(s(x),y) -> f(x,f(x,y))
   f(0(),y) -> c(y,y)
  Restore Modifier:
   DPs:
    f#(s(x),y) -> f#(x,y)
    f#(s(x),y) -> f#(x,f(x,y))
   TRS:
    f(s(x),y) -> f(x,f(x,y))
    f(0(),y) -> c(y,y)
   SCC Processor:
    #sccs: 1
    #rules: 2
    #arcs: 4/4
    DPs:
     f#(s(x),y) -> f#(x,y)
     f#(s(x),y) -> f#(x,f(x,y))
    TRS:
     f(s(x),y) -> f(x,f(x,y))
     f(0(),y) -> c(y,y)
    Matrix Interpretation Processor:
     dimension: 1
     interpretation:
      [f#](x0, x1) = x0 + 1,
      
      [c](x0, x1) = 0,
      
      [0] = 0,
      
      [f](x0, x1) = 0,
      
      [s](x0) = x0 + 1
     orientation:
      f#(s(x),y) = x + 2 >= x + 1 = f#(x,y)
      
      f#(s(x),y) = x + 2 >= x + 1 = f#(x,f(x,y))
      
      f(s(x),y) = 0 >= 0 = f(x,f(x,y))
      
      f(0(),y) = 0 >= 0 = c(y,y)
     problem:
      DPs:
       
      TRS:
       f(s(x),y) -> f(x,f(x,y))
       f(0(),y) -> c(y,y)
     Qed