MAYBE

Problem:
 app(app(fmap(),fnil()),x) -> nil()
 app(app(fmap(),app(app(fcons(),f),t)),x) -> app(app(cons(),app(f,x)),app(app(fmap(),t),x))

Proof:
 DP Processor:
  DPs:
   app#(app(fmap(),app(app(fcons(),f),t)),x) -> app#(fmap(),t)
   app#(app(fmap(),app(app(fcons(),f),t)),x) -> app#(app(fmap(),t),x)
   app#(app(fmap(),app(app(fcons(),f),t)),x) -> app#(f,x)
   app#(app(fmap(),app(app(fcons(),f),t)),x) -> app#(cons(),app(f,x))
   app#(app(fmap(),app(app(fcons(),f),t)),x) -> app#(app(cons(),app(f,x)),app(app(fmap(),t),x))
  TRS:
   app(app(fmap(),fnil()),x) -> nil()
   app(app(fmap(),app(app(fcons(),f),t)),x) -> app(app(cons(),app(f,x)),app(app(fmap(),t),x))
  EDG Processor:
   DPs:
    app#(app(fmap(),app(app(fcons(),f),t)),x) -> app#(fmap(),t)
    app#(app(fmap(),app(app(fcons(),f),t)),x) -> app#(app(fmap(),t),x)
    app#(app(fmap(),app(app(fcons(),f),t)),x) -> app#(f,x)
    app#(app(fmap(),app(app(fcons(),f),t)),x) -> app#(cons(),app(f,x))
    app#(app(fmap(),app(app(fcons(),f),t)),x) -> app#(app(cons(),app(f,x)),app(app(fmap(),t),x))
   TRS:
    app(app(fmap(),fnil()),x) -> nil()
    app(app(fmap(),app(app(fcons(),f),t)),x) -> app(app(cons(),app(f,x)),app(app(fmap(),t),x))
   graph:
    app#(app(fmap(),app(app(fcons(),f),t)),x) -> app#(app(fmap(),t),x) ->
    app#(app(fmap(),app(app(fcons(),f),t)),x) -> app#(fmap(),t)
    app#(app(fmap(),app(app(fcons(),f),t)),x) -> app#(app(fmap(),t),x) ->
    app#(app(fmap(),app(app(fcons(),f),t)),x) -> app#(app(fmap(),t),x)
    app#(app(fmap(),app(app(fcons(),f),t)),x) -> app#(app(fmap(),t),x) ->
    app#(app(fmap(),app(app(fcons(),f),t)),x) -> app#(f,x)
    app#(app(fmap(),app(app(fcons(),f),t)),x) -> app#(app(fmap(),t),x) ->
    app#(app(fmap(),app(app(fcons(),f),t)),x) -> app#(cons(),app(f,x))
    app#(app(fmap(),app(app(fcons(),f),t)),x) -> app#(app(fmap(),t),x) ->
    app#(app(fmap(),app(app(fcons(),f),t)),x) -> app#(app(cons(),app(f,x)),app(app(fmap(),t),x))
    app#(app(fmap(),app(app(fcons(),f),t)),x) -> app#(f,x) ->
    app#(app(fmap(),app(app(fcons(),f),t)),x) -> app#(fmap(),t)
    app#(app(fmap(),app(app(fcons(),f),t)),x) -> app#(f,x) ->
    app#(app(fmap(),app(app(fcons(),f),t)),x) -> app#(app(fmap(),t),x)
    app#(app(fmap(),app(app(fcons(),f),t)),x) -> app#(f,x) ->
    app#(app(fmap(),app(app(fcons(),f),t)),x) -> app#(f,x)
    app#(app(fmap(),app(app(fcons(),f),t)),x) -> app#(f,x) ->
    app#(app(fmap(),app(app(fcons(),f),t)),x) -> app#(cons(),app(f,x))
    app#(app(fmap(),app(app(fcons(),f),t)),x) -> app#(f,x) ->
    app#(app(fmap(),app(app(fcons(),f),t)),x) -> app#(app(cons(),app(f,x)),app(app(fmap(),t),x))
   SCC Processor:
    #sccs: 1
    #rules: 2
    #arcs: 10/25
    DPs:
     app#(app(fmap(),app(app(fcons(),f),t)),x) -> app#(app(fmap(),t),x)
     app#(app(fmap(),app(app(fcons(),f),t)),x) -> app#(f,x)
    TRS:
     app(app(fmap(),fnil()),x) -> nil()
     app(app(fmap(),app(app(fcons(),f),t)),x) -> app(app(cons(),app(f,x)),app(app(fmap(),t),x))
    Open