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))

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))
  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))
  EDG 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))
   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))
   graph:
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs)
    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#(app(map(),f),xs) ->
    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(map(),f),xs) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(cons(),app(f,x)),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#(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#(f,x)
    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#(f,x) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(cons(),app(f,x)),app(app(map(),f),xs))
   SCC Processor:
    #sccs: 1
    #rules: 2
    #arcs: 8/16
    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)
    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))
    Open