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)))
  Usable Rule 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:
    round(s(0())) -> s(0())
    round(s(s(x))) -> s(s(round(x)))
    round(0()) -> 0()
    round(0()) -> s(0())
   CDG 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:
     round(s(0())) -> s(0())
     round(s(s(x))) -> s(s(round(x)))
     round(0()) -> 0()
     round(0()) -> s(0())
    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) -> round#(s(x))
     f#(s(x),x) -> f#(s(x),round(s(x))) -> f#(s(x),x) -> f#(s(x),round(s(x)))
    Restore Modifier:
     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)))
     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)))
      Matrix Interpretation Processor:
       dimension: 1
       interpretation:
        [round#](x0) = x0,
        
        [0] = 0,
        
        [round](x0) = x0 + 1,
        
        [f](x0, x1) = 0,
        
        [s](x0) = x0 + 1
       orientation:
        round#(s(s(x))) = x + 2 >= x = round#(x)
        
        f(s(x),x) = 0 >= 0 = f(s(x),round(s(x)))
        
        round(0()) = 1 >= 0 = 0()
        
        round(0()) = 1 >= 1 = s(0())
        
        round(s(0())) = 2 >= 1 = s(0())
        
        round(s(s(x))) = x + 3 >= x + 3 = s(s(round(x)))
       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