MAYBE

Problem:
 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))
 app(app(minus(),x),0()) -> x
 app(app(minus(),app(s(),x)),app(s(),y)) -> app(app(minus(),x),y)
 app(app(div(),0()),app(s(),y)) -> 0()
 app(app(div(),app(s(),x)),app(s(),y)) -> app(s(),app(app(div(),app(app(minus(),x),y)),app(s(),y)))

Proof:
 DP Processor:
  DPs:
   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))
   app#(app(minus(),app(s(),x)),app(s(),y)) -> app#(minus(),x)
   app#(app(minus(),app(s(),x)),app(s(),y)) -> app#(app(minus(),x),y)
   app#(app(div(),app(s(),x)),app(s(),y)) -> app#(minus(),x)
   app#(app(div(),app(s(),x)),app(s(),y)) -> app#(app(minus(),x),y)
   app#(app(div(),app(s(),x)),app(s(),y)) -> app#(div(),app(app(minus(),x),y))
   app#(app(div(),app(s(),x)),app(s(),y)) -> app#(app(div(),app(app(minus(),x),y)),app(s(),y))
   app#(app(div(),app(s(),x)),app(s(),y)) ->
   app#(s(),app(app(div(),app(app(minus(),x),y)),app(s(),y)))
  TRS:
   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))
   app(app(minus(),x),0()) -> x
   app(app(minus(),app(s(),x)),app(s(),y)) -> app(app(minus(),x),y)
   app(app(div(),0()),app(s(),y)) -> 0()
   app(app(div(),app(s(),x)),app(s(),y)) ->
   app(s(),app(app(div(),app(app(minus(),x),y)),app(s(),y)))
  Open