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(append(),xs),nil()) -> xs
 app(app(append(),nil()),ys) -> ys
 app(app(append(),app(app(cons(),x),xs)),ys) -> app(app(cons(),x),app(app(append(),xs),ys))
 app(app(zip(),nil()),yss) -> yss
 app(app(zip(),xss),nil()) -> xss
 app(app(zip(),app(app(cons(),xs),xss)),app(app(cons(),ys),yss)) ->
 app(app(cons(),app(app(append(),xs),ys)),app(app(zip(),xss),yss))
 app(app(combine(),xs),nil()) -> xs
 app(app(combine(),xs),app(app(cons(),ys),yss)) -> app(app(combine(),app(app(zip(),xs),ys)),yss)
 app(levels(),app(app(node(),x),xs)) ->
 app(app(cons(),app(app(cons(),x),nil())),app(app(combine(),nil()),app(app(map(),levels()),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(append(),app(app(cons(),x),xs)),ys) -> app#(append(),xs)
   app#(app(append(),app(app(cons(),x),xs)),ys) -> app#(app(append(),xs),ys)
   app#(app(append(),app(app(cons(),x),xs)),ys) -> app#(app(cons(),x),app(app(append(),xs),ys))
   app#(app(zip(),app(app(cons(),xs),xss)),app(app(cons(),ys),yss)) -> app#(zip(),xss)
   app#(app(zip(),app(app(cons(),xs),xss)),app(app(cons(),ys),yss)) -> app#(app(zip(),xss),yss)
   app#(app(zip(),app(app(cons(),xs),xss)),app(app(cons(),ys),yss)) -> app#(append(),xs)
   app#(app(zip(),app(app(cons(),xs),xss)),app(app(cons(),ys),yss)) -> app#(app(append(),xs),ys)
   app#(app(zip(),app(app(cons(),xs),xss)),app(app(cons(),ys),yss)) ->
   app#(cons(),app(app(append(),xs),ys))
   app#(app(zip(),app(app(cons(),xs),xss)),app(app(cons(),ys),yss)) ->
   app#(app(cons(),app(app(append(),xs),ys)),app(app(zip(),xss),yss))
   app#(app(combine(),xs),app(app(cons(),ys),yss)) -> app#(zip(),xs)
   app#(app(combine(),xs),app(app(cons(),ys),yss)) -> app#(app(zip(),xs),ys)
   app#(app(combine(),xs),app(app(cons(),ys),yss)) -> app#(combine(),app(app(zip(),xs),ys))
   app#(app(combine(),xs),app(app(cons(),ys),yss)) ->
   app#(app(combine(),app(app(zip(),xs),ys)),yss)
   app#(levels(),app(app(node(),x),xs)) -> app#(map(),levels())
   app#(levels(),app(app(node(),x),xs)) -> app#(app(map(),levels()),xs)
   app#(levels(),app(app(node(),x),xs)) -> app#(combine(),nil())
   app#(levels(),app(app(node(),x),xs)) -> app#(app(combine(),nil()),app(app(map(),levels()),xs))
   app#(levels(),app(app(node(),x),xs)) -> app#(cons(),x)
   app#(levels(),app(app(node(),x),xs)) -> app#(app(cons(),x),nil())
   app#(levels(),app(app(node(),x),xs)) -> app#(cons(),app(app(cons(),x),nil()))
   app#(levels(),app(app(node(),x),xs)) ->
   app#(app(cons(),app(app(cons(),x),nil())),app(app(combine(),nil()),app(app(map(),levels()),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(append(),xs),nil()) -> xs
   app(app(append(),nil()),ys) -> ys
   app(app(append(),app(app(cons(),x),xs)),ys) -> app(app(cons(),x),app(app(append(),xs),ys))
   app(app(zip(),nil()),yss) -> yss
   app(app(zip(),xss),nil()) -> xss
   app(app(zip(),app(app(cons(),xs),xss)),app(app(cons(),ys),yss)) ->
   app(app(cons(),app(app(append(),xs),ys)),app(app(zip(),xss),yss))
   app(app(combine(),xs),nil()) -> xs
   app(app(combine(),xs),app(app(cons(),ys),yss)) -> app(app(combine(),app(app(zip(),xs),ys)),yss)
   app(levels(),app(app(node(),x),xs)) ->
   app(app(cons(),app(app(cons(),x),nil())),app(app(combine(),nil()),app(app(map(),levels()),xs)))
  Open