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(treemap(),f),app(app(node(),x),xs)) ->
 app(app(node(),app(f,x)),app(app(map(),app(treemap(),f)),xs))

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(treemap(),f),app(app(node(),x),xs)) -> app#(map(),app(treemap(),f))
   app#(app(treemap(),f),app(app(node(),x),xs)) -> app#(app(map(),app(treemap(),f)),xs)
   app#(app(treemap(),f),app(app(node(),x),xs)) -> app#(f,x)
   app#(app(treemap(),f),app(app(node(),x),xs)) -> app#(node(),app(f,x))
   app#(app(treemap(),f),app(app(node(),x),xs)) ->
   app#(app(node(),app(f,x)),app(app(map(),app(treemap(),f)),xs))
  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(treemap(),f),app(app(node(),x),xs)) ->
   app(app(node(),app(f,x)),app(app(map(),app(treemap(),f)),xs))
  Open