MAYBE

Problem:
 purge(nil()) -> nil()
 purge(.(x,y)) -> .(x,purge(remove(x,y)))
 remove(x,nil()) -> nil()
 remove(x,.(y,z)) -> if(=(x,y),remove(x,z),.(y,remove(x,z)))

Proof:
 DP Processor:
  DPs:
   purge#(.(x,y)) -> remove#(x,y)
   purge#(.(x,y)) -> purge#(remove(x,y))
   remove#(x,.(y,z)) -> remove#(x,z)
  TRS:
   purge(nil()) -> nil()
   purge(.(x,y)) -> .(x,purge(remove(x,y)))
   remove(x,nil()) -> nil()
   remove(x,.(y,z)) -> if(=(x,y),remove(x,z),.(y,remove(x,z)))
  Usable Rule Processor:
   DPs:
    purge#(.(x,y)) -> remove#(x,y)
    purge#(.(x,y)) -> purge#(remove(x,y))
    remove#(x,.(y,z)) -> remove#(x,z)
   TRS:
    f8(x,y) -> x
    f8(x,y) -> y
    remove(x,nil()) -> nil()
    remove(x,.(y,z)) -> if(=(x,y),remove(x,z),.(y,remove(x,z)))
   TDG Processor:
    DPs:
     purge#(.(x,y)) -> remove#(x,y)
     purge#(.(x,y)) -> purge#(remove(x,y))
     remove#(x,.(y,z)) -> remove#(x,z)
    TRS:
     f8(x,y) -> x
     f8(x,y) -> y
     remove(x,nil()) -> nil()
     remove(x,.(y,z)) -> if(=(x,y),remove(x,z),.(y,remove(x,z)))
    graph:
     remove#(x,.(y,z)) -> remove#(x,z) ->
     remove#(x,.(y,z)) -> remove#(x,z)
     purge#(.(x,y)) -> remove#(x,y) ->
     remove#(x,.(y,z)) -> remove#(x,z)
     purge#(.(x,y)) -> purge#(remove(x,y)) ->
     purge#(.(x,y)) -> purge#(remove(x,y))
     purge#(.(x,y)) -> purge#(remove(x,y)) -> purge#(.(x,y)) -> remove#(x,y)
    Restore Modifier:
     DPs:
      purge#(.(x,y)) -> remove#(x,y)
      purge#(.(x,y)) -> purge#(remove(x,y))
      remove#(x,.(y,z)) -> remove#(x,z)
     TRS:
      purge(nil()) -> nil()
      purge(.(x,y)) -> .(x,purge(remove(x,y)))
      remove(x,nil()) -> nil()
      remove(x,.(y,z)) -> if(=(x,y),remove(x,z),.(y,remove(x,z)))
     SCC Processor:
      #sccs: 2
      #rules: 2
      #arcs: 4/9
      DPs:
       purge#(.(x,y)) -> purge#(remove(x,y))
      TRS:
       purge(nil()) -> nil()
       purge(.(x,y)) -> .(x,purge(remove(x,y)))
       remove(x,nil()) -> nil()
       remove(x,.(y,z)) -> if(=(x,y),remove(x,z),.(y,remove(x,z)))
      Open
      
      DPs:
       remove#(x,.(y,z)) -> remove#(x,z)
      TRS:
       purge(nil()) -> nil()
       purge(.(x,y)) -> .(x,purge(remove(x,y)))
       remove(x,nil()) -> nil()
       remove(x,.(y,z)) -> if(=(x,y),remove(x,z),.(y,remove(x,z)))
      Open