MAYBE

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

Proof:
 DP Processor:
  DPs:
   f#(s(0()),y,z) -> f#(0(),s(y),s(z))
   f#(s(x),s(y),0()) -> f#(x,y,s(0()))
   f#(s(x),0(),s(z)) -> f#(x,s(0()),z)
   f#(s(x),s(y),s(z)) -> f#(s(x),s(y),z)
   f#(s(x),s(y),s(z)) -> f#(x,y,f(s(x),s(y),z))
   f#(0(),s(s(y)),s(0())) -> f#(0(),y,s(0()))
   f#(0(),s(0()),s(s(z))) -> f#(0(),s(0()),z)
   f#(0(),s(s(y)),s(s(z))) -> f#(0(),s(s(y)),s(z))
   f#(0(),s(s(y)),s(s(z))) -> f#(0(),y,f(0(),s(s(y)),s(z)))
  TRS:
   f(x,0(),0()) -> s(x)
   f(0(),y,0()) -> s(y)
   f(0(),0(),z) -> s(z)
   f(s(0()),y,z) -> f(0(),s(y),s(z))
   f(s(x),s(y),0()) -> f(x,y,s(0()))
   f(s(x),0(),s(z)) -> f(x,s(0()),z)
   f(0(),s(0()),s(0())) -> s(s(0()))
   f(s(x),s(y),s(z)) -> f(x,y,f(s(x),s(y),z))
   f(0(),s(s(y)),s(0())) -> f(0(),y,s(0()))
   f(0(),s(0()),s(s(z))) -> f(0(),s(0()),z)
   f(0(),s(s(y)),s(s(z))) -> f(0(),y,f(0(),s(s(y)),s(z)))
  EDG Processor:
   DPs:
    f#(s(0()),y,z) -> f#(0(),s(y),s(z))
    f#(s(x),s(y),0()) -> f#(x,y,s(0()))
    f#(s(x),0(),s(z)) -> f#(x,s(0()),z)
    f#(s(x),s(y),s(z)) -> f#(s(x),s(y),z)
    f#(s(x),s(y),s(z)) -> f#(x,y,f(s(x),s(y),z))
    f#(0(),s(s(y)),s(0())) -> f#(0(),y,s(0()))
    f#(0(),s(0()),s(s(z))) -> f#(0(),s(0()),z)
    f#(0(),s(s(y)),s(s(z))) -> f#(0(),s(s(y)),s(z))
    f#(0(),s(s(y)),s(s(z))) -> f#(0(),y,f(0(),s(s(y)),s(z)))
   TRS:
    f(x,0(),0()) -> s(x)
    f(0(),y,0()) -> s(y)
    f(0(),0(),z) -> s(z)
    f(s(0()),y,z) -> f(0(),s(y),s(z))
    f(s(x),s(y),0()) -> f(x,y,s(0()))
    f(s(x),0(),s(z)) -> f(x,s(0()),z)
    f(0(),s(0()),s(0())) -> s(s(0()))
    f(s(x),s(y),s(z)) -> f(x,y,f(s(x),s(y),z))
    f(0(),s(s(y)),s(0())) -> f(0(),y,s(0()))
    f(0(),s(0()),s(s(z))) -> f(0(),s(0()),z)
    f(0(),s(s(y)),s(s(z))) -> f(0(),y,f(0(),s(s(y)),s(z)))
   graph:
    f#(s(0()),y,z) -> f#(0(),s(y),s(z)) ->
    f#(0(),s(s(y)),s(0())) -> f#(0(),y,s(0()))
    f#(s(0()),y,z) -> f#(0(),s(y),s(z)) ->
    f#(0(),s(0()),s(s(z))) -> f#(0(),s(0()),z)
    f#(s(0()),y,z) -> f#(0(),s(y),s(z)) ->
    f#(0(),s(s(y)),s(s(z))) -> f#(0(),s(s(y)),s(z))
    f#(s(0()),y,z) -> f#(0(),s(y),s(z)) ->
    f#(0(),s(s(y)),s(s(z))) -> f#(0(),y,f(0(),s(s(y)),s(z)))
    f#(s(x),s(y),s(z)) -> f#(s(x),s(y),z) ->
    f#(s(0()),y,z) -> f#(0(),s(y),s(z))
    f#(s(x),s(y),s(z)) -> f#(s(x),s(y),z) ->
    f#(s(x),s(y),0()) -> f#(x,y,s(0()))
    f#(s(x),s(y),s(z)) -> f#(s(x),s(y),z) ->
    f#(s(x),s(y),s(z)) -> f#(s(x),s(y),z)
    f#(s(x),s(y),s(z)) -> f#(s(x),s(y),z) ->
    f#(s(x),s(y),s(z)) -> f#(x,y,f(s(x),s(y),z))
    f#(s(x),s(y),s(z)) -> f#(x,y,f(s(x),s(y),z)) ->
    f#(s(0()),y,z) -> f#(0(),s(y),s(z))
    f#(s(x),s(y),s(z)) -> f#(x,y,f(s(x),s(y),z)) ->
    f#(s(x),0(),s(z)) -> f#(x,s(0()),z)
    f#(s(x),s(y),s(z)) -> f#(x,y,f(s(x),s(y),z)) ->
    f#(s(x),s(y),s(z)) -> f#(s(x),s(y),z)
    f#(s(x),s(y),s(z)) -> f#(x,y,f(s(x),s(y),z)) ->
    f#(s(x),s(y),s(z)) -> f#(x,y,f(s(x),s(y),z))
    f#(s(x),s(y),s(z)) -> f#(x,y,f(s(x),s(y),z)) ->
    f#(0(),s(s(y)),s(0())) -> f#(0(),y,s(0()))
    f#(s(x),s(y),s(z)) -> f#(x,y,f(s(x),s(y),z)) ->
    f#(0(),s(0()),s(s(z))) -> f#(0(),s(0()),z)
    f#(s(x),s(y),s(z)) -> f#(x,y,f(s(x),s(y),z)) ->
    f#(0(),s(s(y)),s(s(z))) -> f#(0(),s(s(y)),s(z))
    f#(s(x),s(y),s(z)) -> f#(x,y,f(s(x),s(y),z)) ->
    f#(0(),s(s(y)),s(s(z))) -> f#(0(),y,f(0(),s(s(y)),s(z)))
    f#(s(x),s(y),0()) -> f#(x,y,s(0())) ->
    f#(s(0()),y,z) -> f#(0(),s(y),s(z))
    f#(s(x),s(y),0()) -> f#(x,y,s(0())) ->
    f#(s(x),0(),s(z)) -> f#(x,s(0()),z)
    f#(s(x),s(y),0()) -> f#(x,y,s(0())) ->
    f#(s(x),s(y),s(z)) -> f#(s(x),s(y),z)
    f#(s(x),s(y),0()) -> f#(x,y,s(0())) ->
    f#(s(x),s(y),s(z)) -> f#(x,y,f(s(x),s(y),z))
    f#(s(x),s(y),0()) -> f#(x,y,s(0())) ->
    f#(0(),s(s(y)),s(0())) -> f#(0(),y,s(0()))
    f#(s(x),0(),s(z)) -> f#(x,s(0()),z) ->
    f#(s(0()),y,z) -> f#(0(),s(y),s(z))
    f#(s(x),0(),s(z)) -> f#(x,s(0()),z) ->
    f#(s(x),s(y),0()) -> f#(x,y,s(0()))
    f#(s(x),0(),s(z)) -> f#(x,s(0()),z) ->
    f#(s(x),s(y),s(z)) -> f#(s(x),s(y),z)
    f#(s(x),0(),s(z)) -> f#(x,s(0()),z) ->
    f#(s(x),s(y),s(z)) -> f#(x,y,f(s(x),s(y),z))
    f#(s(x),0(),s(z)) -> f#(x,s(0()),z) ->
    f#(0(),s(0()),s(s(z))) -> f#(0(),s(0()),z)
    f#(0(),s(s(y)),s(s(z))) -> f#(0(),s(s(y)),s(z)) ->
    f#(0(),s(s(y)),s(0())) -> f#(0(),y,s(0()))
    f#(0(),s(s(y)),s(s(z))) -> f#(0(),s(s(y)),s(z)) ->
    f#(0(),s(s(y)),s(s(z))) -> f#(0(),s(s(y)),s(z))
    f#(0(),s(s(y)),s(s(z))) -> f#(0(),s(s(y)),s(z)) ->
    f#(0(),s(s(y)),s(s(z))) -> f#(0(),y,f(0(),s(s(y)),s(z)))
    f#(0(),s(s(y)),s(s(z))) -> f#(0(),y,f(0(),s(s(y)),s(z))) ->
    f#(0(),s(s(y)),s(0())) -> f#(0(),y,s(0()))
    f#(0(),s(s(y)),s(s(z))) -> f#(0(),y,f(0(),s(s(y)),s(z))) ->
    f#(0(),s(0()),s(s(z))) -> f#(0(),s(0()),z)
    f#(0(),s(s(y)),s(s(z))) -> f#(0(),y,f(0(),s(s(y)),s(z))) ->
    f#(0(),s(s(y)),s(s(z))) -> f#(0(),s(s(y)),s(z))
    f#(0(),s(s(y)),s(s(z))) -> f#(0(),y,f(0(),s(s(y)),s(z))) ->
    f#(0(),s(s(y)),s(s(z))) -> f#(0(),y,f(0(),s(s(y)),s(z)))
    f#(0(),s(s(y)),s(0())) -> f#(0(),y,s(0())) ->
    f#(0(),s(s(y)),s(0())) -> f#(0(),y,s(0()))
    f#(0(),s(0()),s(s(z))) -> f#(0(),s(0()),z) -> f#(0(),s(0()),s(s(z))) -> f#(0(),s(0()),z)
   SCC Processor:
    #sccs: 4
    #rules: 8
    #arcs: 35/81
    DPs:
     f#(s(x),s(y),s(z)) -> f#(s(x),s(y),z)
     f#(s(x),s(y),s(z)) -> f#(x,y,f(s(x),s(y),z))
     f#(s(x),0(),s(z)) -> f#(x,s(0()),z)
     f#(s(x),s(y),0()) -> f#(x,y,s(0()))
    TRS:
     f(x,0(),0()) -> s(x)
     f(0(),y,0()) -> s(y)
     f(0(),0(),z) -> s(z)
     f(s(0()),y,z) -> f(0(),s(y),s(z))
     f(s(x),s(y),0()) -> f(x,y,s(0()))
     f(s(x),0(),s(z)) -> f(x,s(0()),z)
     f(0(),s(0()),s(0())) -> s(s(0()))
     f(s(x),s(y),s(z)) -> f(x,y,f(s(x),s(y),z))
     f(0(),s(s(y)),s(0())) -> f(0(),y,s(0()))
     f(0(),s(0()),s(s(z))) -> f(0(),s(0()),z)
     f(0(),s(s(y)),s(s(z))) -> f(0(),y,f(0(),s(s(y)),s(z)))
    Open
    
    DPs:
     f#(0(),s(s(y)),s(s(z))) -> f#(0(),y,f(0(),s(s(y)),s(z)))
     f#(0(),s(s(y)),s(s(z))) -> f#(0(),s(s(y)),s(z))
    TRS:
     f(x,0(),0()) -> s(x)
     f(0(),y,0()) -> s(y)
     f(0(),0(),z) -> s(z)
     f(s(0()),y,z) -> f(0(),s(y),s(z))
     f(s(x),s(y),0()) -> f(x,y,s(0()))
     f(s(x),0(),s(z)) -> f(x,s(0()),z)
     f(0(),s(0()),s(0())) -> s(s(0()))
     f(s(x),s(y),s(z)) -> f(x,y,f(s(x),s(y),z))
     f(0(),s(s(y)),s(0())) -> f(0(),y,s(0()))
     f(0(),s(0()),s(s(z))) -> f(0(),s(0()),z)
     f(0(),s(s(y)),s(s(z))) -> f(0(),y,f(0(),s(s(y)),s(z)))
    Open
    
    DPs:
     f#(0(),s(0()),s(s(z))) -> f#(0(),s(0()),z)
    TRS:
     f(x,0(),0()) -> s(x)
     f(0(),y,0()) -> s(y)
     f(0(),0(),z) -> s(z)
     f(s(0()),y,z) -> f(0(),s(y),s(z))
     f(s(x),s(y),0()) -> f(x,y,s(0()))
     f(s(x),0(),s(z)) -> f(x,s(0()),z)
     f(0(),s(0()),s(0())) -> s(s(0()))
     f(s(x),s(y),s(z)) -> f(x,y,f(s(x),s(y),z))
     f(0(),s(s(y)),s(0())) -> f(0(),y,s(0()))
     f(0(),s(0()),s(s(z))) -> f(0(),s(0()),z)
     f(0(),s(s(y)),s(s(z))) -> f(0(),y,f(0(),s(s(y)),s(z)))
    LPO Processor:
     argument filtering:
      pi(0) = []
      pi(f) = [0,1,2]
      pi(s) = [0]
      pi(f#) = 2
     precedence:
      f > f# ~ s ~ 0
     problem:
      DPs:
       
      TRS:
       f(x,0(),0()) -> s(x)
       f(0(),y,0()) -> s(y)
       f(0(),0(),z) -> s(z)
       f(s(0()),y,z) -> f(0(),s(y),s(z))
       f(s(x),s(y),0()) -> f(x,y,s(0()))
       f(s(x),0(),s(z)) -> f(x,s(0()),z)
       f(0(),s(0()),s(0())) -> s(s(0()))
       f(s(x),s(y),s(z)) -> f(x,y,f(s(x),s(y),z))
       f(0(),s(s(y)),s(0())) -> f(0(),y,s(0()))
       f(0(),s(0()),s(s(z))) -> f(0(),s(0()),z)
       f(0(),s(s(y)),s(s(z))) -> f(0(),y,f(0(),s(s(y)),s(z)))
     Qed
    
    DPs:
     f#(0(),s(s(y)),s(0())) -> f#(0(),y,s(0()))
    TRS:
     f(x,0(),0()) -> s(x)
     f(0(),y,0()) -> s(y)
     f(0(),0(),z) -> s(z)
     f(s(0()),y,z) -> f(0(),s(y),s(z))
     f(s(x),s(y),0()) -> f(x,y,s(0()))
     f(s(x),0(),s(z)) -> f(x,s(0()),z)
     f(0(),s(0()),s(0())) -> s(s(0()))
     f(s(x),s(y),s(z)) -> f(x,y,f(s(x),s(y),z))
     f(0(),s(s(y)),s(0())) -> f(0(),y,s(0()))
     f(0(),s(0()),s(s(z))) -> f(0(),s(0()),z)
     f(0(),s(s(y)),s(s(z))) -> f(0(),y,f(0(),s(s(y)),s(z)))
    LPO Processor:
     argument filtering:
      pi(0) = []
      pi(f) = [0,1,2]
      pi(s) = [0]
      pi(f#) = 1
     precedence:
      f > f# ~ s ~ 0
     problem:
      DPs:
       
      TRS:
       f(x,0(),0()) -> s(x)
       f(0(),y,0()) -> s(y)
       f(0(),0(),z) -> s(z)
       f(s(0()),y,z) -> f(0(),s(y),s(z))
       f(s(x),s(y),0()) -> f(x,y,s(0()))
       f(s(x),0(),s(z)) -> f(x,s(0()),z)
       f(0(),s(0()),s(0())) -> s(s(0()))
       f(s(x),s(y),s(z)) -> f(x,y,f(s(x),s(y),z))
       f(0(),s(s(y)),s(0())) -> f(0(),y,s(0()))
       f(0(),s(0()),s(s(z))) -> f(0(),s(0()),z)
       f(0(),s(s(y)),s(s(z))) -> f(0(),y,f(0(),s(s(y)),s(z)))
     Qed