MAYBE

Problem:
 app(app(mapt(),f),app(leaf(),x)) -> app(leaf(),app(f,x))
 app(app(mapt(),f),app(node(),xs)) -> app(node(),app(app(maptlist(),f),xs))
 app(app(maptlist(),f),nil()) -> nil()
 app(app(maptlist(),f),app(app(cons(),x),xs)) ->
 app(app(cons(),app(app(mapt(),f),x)),app(app(maptlist(),f),xs))

Proof:
 DP Processor:
  DPs:
   app#(app(mapt(),f),app(leaf(),x)) -> app#(f,x)
   app#(app(mapt(),f),app(leaf(),x)) -> app#(leaf(),app(f,x))
   app#(app(mapt(),f),app(node(),xs)) -> app#(maptlist(),f)
   app#(app(mapt(),f),app(node(),xs)) -> app#(app(maptlist(),f),xs)
   app#(app(mapt(),f),app(node(),xs)) -> app#(node(),app(app(maptlist(),f),xs))
   app#(app(maptlist(),f),app(app(cons(),x),xs)) -> app#(app(maptlist(),f),xs)
   app#(app(maptlist(),f),app(app(cons(),x),xs)) -> app#(mapt(),f)
   app#(app(maptlist(),f),app(app(cons(),x),xs)) -> app#(app(mapt(),f),x)
   app#(app(maptlist(),f),app(app(cons(),x),xs)) -> app#(cons(),app(app(mapt(),f),x))
   app#(app(maptlist(),f),app(app(cons(),x),xs)) ->
   app#(app(cons(),app(app(mapt(),f),x)),app(app(maptlist(),f),xs))
  TRS:
   app(app(mapt(),f),app(leaf(),x)) -> app(leaf(),app(f,x))
   app(app(mapt(),f),app(node(),xs)) -> app(node(),app(app(maptlist(),f),xs))
   app(app(maptlist(),f),nil()) -> nil()
   app(app(maptlist(),f),app(app(cons(),x),xs)) ->
   app(app(cons(),app(app(mapt(),f),x)),app(app(maptlist(),f),xs))
  Open