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)))
   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)))
    KBO Processor:
     argument filtering:
      pi(c) = [0]
      pi(f) = []
      pi(s) = [0]
      pi(f#) = 1
     weight function:
      w0 = 1
      w(f#) = w(s) = w(f) = w(c) = 1
     precedence:
      f# ~ s ~ f ~ c
     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)))
    KBO Processor:
     argument filtering:
      pi(c) = []
      pi(f) = []
      pi(s) = [0]
      pi(f#) = [0,1]
     weight function:
      w0 = 1
      w(f#) = w(f) = w(c) = 1
      w(s) = 0
     precedence:
      f# ~ s ~ f ~ c
     problem:
      DPs:
       
      TRS:
       f(x,c(y)) -> f(x,s(f(y,y)))
       f(s(x),y) -> f(x,s(c(y)))
     Qed