MAYBE

Problem:
 app(app(f,0()),n) -> app(app(hd(),app(app(map(),f),app(app(cons(),0()),nil()))),n)
 app(app(map(),f),nil()) -> nil()
 app(app(map(),f),app(app(cons(),x),xs)) -> app(app(cons(),app(f,x)),app(app(map(),f),xs))

Proof:
 DP Processor:
  DPs:
   app#(app(f,0()),n) -> app#(cons(),0())
   app#(app(f,0()),n) -> app#(app(cons(),0()),nil())
   app#(app(f,0()),n) -> app#(map(),f)
   app#(app(f,0()),n) -> app#(app(map(),f),app(app(cons(),0()),nil()))
   app#(app(f,0()),n) -> app#(hd(),app(app(map(),f),app(app(cons(),0()),nil())))
   app#(app(f,0()),n) -> app#(app(hd(),app(app(map(),f),app(app(cons(),0()),nil()))),n)
   app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs)
   app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x)
   app#(app(map(),f),app(app(cons(),x),xs)) -> app#(cons(),app(f,x))
   app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(cons(),app(f,x)),app(app(map(),f),xs))
  TRS:
   app(app(f,0()),n) -> app(app(hd(),app(app(map(),f),app(app(cons(),0()),nil()))),n)
   app(app(map(),f),nil()) -> nil()
   app(app(map(),f),app(app(cons(),x),xs)) -> app(app(cons(),app(f,x)),app(app(map(),f),xs))
  Open