MAYBE

Problem:
 f(s(x),x) -> f(s(x),round(s(x)))
 round(0()) -> 0()
 round(0()) -> s(0())
 round(s(0())) -> s(0())
 round(s(s(x))) -> s(s(round(x)))

Proof:
 DP Processor:
  DPs:
   f#(s(x),x) -> round#(s(x))
   f#(s(x),x) -> f#(s(x),round(s(x)))
   round#(s(s(x))) -> round#(x)
  TRS:
   f(s(x),x) -> f(s(x),round(s(x)))
   round(0()) -> 0()
   round(0()) -> s(0())
   round(s(0())) -> s(0())
   round(s(s(x))) -> s(s(round(x)))
  TDG Processor:
   DPs:
    f#(s(x),x) -> round#(s(x))
    f#(s(x),x) -> f#(s(x),round(s(x)))
    round#(s(s(x))) -> round#(x)
   TRS:
    f(s(x),x) -> f(s(x),round(s(x)))
    round(0()) -> 0()
    round(0()) -> s(0())
    round(s(0())) -> s(0())
    round(s(s(x))) -> s(s(round(x)))
   graph:
    round#(s(s(x))) -> round#(x) -> round#(s(s(x))) -> round#(x)
    f#(s(x),x) -> round#(s(x)) -> round#(s(s(x))) -> round#(x)
    f#(s(x),x) -> f#(s(x),round(s(x))) ->
    f#(s(x),x) -> f#(s(x),round(s(x)))
    f#(s(x),x) -> f#(s(x),round(s(x))) -> f#(s(x),x) -> round#(s(x))
   SCC Processor:
    #sccs: 2
    #rules: 2
    #arcs: 4/9
    DPs:
     f#(s(x),x) -> f#(s(x),round(s(x)))
    TRS:
     f(s(x),x) -> f(s(x),round(s(x)))
     round(0()) -> 0()
     round(0()) -> s(0())
     round(s(0())) -> s(0())
     round(s(s(x))) -> s(s(round(x)))
    Open
    
    DPs:
     round#(s(s(x))) -> round#(x)
    TRS:
     f(s(x),x) -> f(s(x),round(s(x)))
     round(0()) -> 0()
     round(0()) -> s(0())
     round(s(0())) -> s(0())
     round(s(s(x))) -> s(s(round(x)))
    KBO Processor:
     argument filtering:
      pi(s) = [0]
      pi(f) = 0
      pi(round) = [0]
      pi(0) = []
      pi(round#) = 0
     weight function:
      w0 = 1
      w(round#) = w(0) = w(round) = w(f) = w(s) = 1
     precedence:
      round# ~ round > 0 ~ f ~ s
     problem:
      DPs:
       
      TRS:
       f(s(x),x) -> f(s(x),round(s(x)))
       round(0()) -> 0()
       round(0()) -> s(0())
       round(s(0())) -> s(0())
       round(s(s(x))) -> s(s(round(x)))
     Qed