MAYBE

Problem:
 app(app(twice(),f),x) -> app(f,app(f,x))
 app(app(map(),f),nil()) -> nil()
 app(app(map(),f),app(app(cons(),h),t)) -> app(app(cons(),app(f,h)),app(app(map(),f),t))
 app(app(fmap(),nil()),x) -> nil()
 app(app(fmap(),app(app(cons(),f),t_f())),x) -> app(app(cons(),app(f,x)),app(app(fmap(),t_f()),x))

Proof:
 DP Processor:
  DPs:
   app#(app(twice(),f),x) -> app#(f,x)
   app#(app(twice(),f),x) -> app#(f,app(f,x))
   app#(app(map(),f),app(app(cons(),h),t)) -> app#(app(map(),f),t)
   app#(app(map(),f),app(app(cons(),h),t)) -> app#(f,h)
   app#(app(map(),f),app(app(cons(),h),t)) -> app#(cons(),app(f,h))
   app#(app(map(),f),app(app(cons(),h),t)) -> app#(app(cons(),app(f,h)),app(app(map(),f),t))
   app#(app(fmap(),app(app(cons(),f),t_f())),x) -> app#(fmap(),t_f())
   app#(app(fmap(),app(app(cons(),f),t_f())),x) -> app#(app(fmap(),t_f()),x)
   app#(app(fmap(),app(app(cons(),f),t_f())),x) -> app#(f,x)
   app#(app(fmap(),app(app(cons(),f),t_f())),x) -> app#(cons(),app(f,x))
   app#(app(fmap(),app(app(cons(),f),t_f())),x) ->
   app#(app(cons(),app(f,x)),app(app(fmap(),t_f()),x))
  TRS:
   app(app(twice(),f),x) -> app(f,app(f,x))
   app(app(map(),f),nil()) -> nil()
   app(app(map(),f),app(app(cons(),h),t)) -> app(app(cons(),app(f,h)),app(app(map(),f),t))
   app(app(fmap(),nil()),x) -> nil()
   app(app(fmap(),app(app(cons(),f),t_f())),x) ->
   app(app(cons(),app(f,x)),app(app(fmap(),t_f()),x))
  EDG Processor:
   DPs:
    app#(app(twice(),f),x) -> app#(f,x)
    app#(app(twice(),f),x) -> app#(f,app(f,x))
    app#(app(map(),f),app(app(cons(),h),t)) -> app#(app(map(),f),t)
    app#(app(map(),f),app(app(cons(),h),t)) -> app#(f,h)
    app#(app(map(),f),app(app(cons(),h),t)) -> app#(cons(),app(f,h))
    app#(app(map(),f),app(app(cons(),h),t)) -> app#(app(cons(),app(f,h)),app(app(map(),f),t))
    app#(app(fmap(),app(app(cons(),f),t_f())),x) -> app#(fmap(),t_f())
    app#(app(fmap(),app(app(cons(),f),t_f())),x) -> app#(app(fmap(),t_f()),x)
    app#(app(fmap(),app(app(cons(),f),t_f())),x) -> app#(f,x)
    app#(app(fmap(),app(app(cons(),f),t_f())),x) -> app#(cons(),app(f,x))
    app#(app(fmap(),app(app(cons(),f),t_f())),x) ->
    app#(app(cons(),app(f,x)),app(app(fmap(),t_f()),x))
   TRS:
    app(app(twice(),f),x) -> app(f,app(f,x))
    app(app(map(),f),nil()) -> nil()
    app(app(map(),f),app(app(cons(),h),t)) -> app(app(cons(),app(f,h)),app(app(map(),f),t))
    app(app(fmap(),nil()),x) -> nil()
    app(app(fmap(),app(app(cons(),f),t_f())),x) ->
    app(app(cons(),app(f,x)),app(app(fmap(),t_f()),x))
   graph:
    app#(app(fmap(),app(app(cons(),f),t_f())),x) -> app#(f,x) ->
    app#(app(twice(),f),x) -> app#(f,x)
    app#(app(fmap(),app(app(cons(),f),t_f())),x) -> app#(f,x) ->
    app#(app(twice(),f),x) -> app#(f,app(f,x))
    app#(app(fmap(),app(app(cons(),f),t_f())),x) -> app#(f,x) ->
    app#(app(map(),f),app(app(cons(),h),t)) -> app#(app(map(),f),t)
    app#(app(fmap(),app(app(cons(),f),t_f())),x) -> app#(f,x) ->
    app#(app(map(),f),app(app(cons(),h),t)) -> app#(f,h)
    app#(app(fmap(),app(app(cons(),f),t_f())),x) -> app#(f,x) ->
    app#(app(map(),f),app(app(cons(),h),t)) -> app#(cons(),app(f,h))
    app#(app(fmap(),app(app(cons(),f),t_f())),x) -> app#(f,x) ->
    app#(app(map(),f),app(app(cons(),h),t)) -> app#(app(cons(),app(f,h)),app(app(map(),f),t))
    app#(app(fmap(),app(app(cons(),f),t_f())),x) -> app#(f,x) ->
    app#(app(fmap(),app(app(cons(),f),t_f())),x) -> app#(fmap(),t_f())
    app#(app(fmap(),app(app(cons(),f),t_f())),x) -> app#(f,x) ->
    app#(app(fmap(),app(app(cons(),f),t_f())),x) -> app#(app(fmap(),t_f()),x)
    app#(app(fmap(),app(app(cons(),f),t_f())),x) -> app#(f,x) ->
    app#(app(fmap(),app(app(cons(),f),t_f())),x) -> app#(f,x)
    app#(app(fmap(),app(app(cons(),f),t_f())),x) -> app#(f,x) ->
    app#(app(fmap(),app(app(cons(),f),t_f())),x) -> app#(cons(),app(f,x))
    app#(app(fmap(),app(app(cons(),f),t_f())),x) -> app#(f,x) ->
    app#(app(fmap(),app(app(cons(),f),t_f())),x) ->
    app#(app(cons(),app(f,x)),app(app(fmap(),t_f()),x))
    app#(app(map(),f),app(app(cons(),h),t)) -> app#(app(map(),f),t) ->
    app#(app(map(),f),app(app(cons(),h),t)) -> app#(app(map(),f),t)
    app#(app(map(),f),app(app(cons(),h),t)) -> app#(app(map(),f),t) ->
    app#(app(map(),f),app(app(cons(),h),t)) -> app#(f,h)
    app#(app(map(),f),app(app(cons(),h),t)) -> app#(app(map(),f),t) ->
    app#(app(map(),f),app(app(cons(),h),t)) -> app#(cons(),app(f,h))
    app#(app(map(),f),app(app(cons(),h),t)) -> app#(app(map(),f),t) ->
    app#(app(map(),f),app(app(cons(),h),t)) -> app#(app(cons(),app(f,h)),app(app(map(),f),t))
    app#(app(map(),f),app(app(cons(),h),t)) -> app#(f,h) ->
    app#(app(twice(),f),x) -> app#(f,x)
    app#(app(map(),f),app(app(cons(),h),t)) -> app#(f,h) ->
    app#(app(twice(),f),x) -> app#(f,app(f,x))
    app#(app(map(),f),app(app(cons(),h),t)) -> app#(f,h) ->
    app#(app(map(),f),app(app(cons(),h),t)) -> app#(app(map(),f),t)
    app#(app(map(),f),app(app(cons(),h),t)) -> app#(f,h) ->
    app#(app(map(),f),app(app(cons(),h),t)) -> app#(f,h)
    app#(app(map(),f),app(app(cons(),h),t)) -> app#(f,h) ->
    app#(app(map(),f),app(app(cons(),h),t)) -> app#(cons(),app(f,h))
    app#(app(map(),f),app(app(cons(),h),t)) -> app#(f,h) ->
    app#(app(map(),f),app(app(cons(),h),t)) -> app#(app(cons(),app(f,h)),app(app(map(),f),t))
    app#(app(map(),f),app(app(cons(),h),t)) -> app#(f,h) ->
    app#(app(fmap(),app(app(cons(),f),t_f())),x) -> app#(fmap(),t_f())
    app#(app(map(),f),app(app(cons(),h),t)) -> app#(f,h) ->
    app#(app(fmap(),app(app(cons(),f),t_f())),x) -> app#(app(fmap(),t_f()),x)
    app#(app(map(),f),app(app(cons(),h),t)) -> app#(f,h) ->
    app#(app(fmap(),app(app(cons(),f),t_f())),x) -> app#(f,x)
    app#(app(map(),f),app(app(cons(),h),t)) -> app#(f,h) ->
    app#(app(fmap(),app(app(cons(),f),t_f())),x) -> app#(cons(),app(f,x))
    app#(app(map(),f),app(app(cons(),h),t)) -> app#(f,h) ->
    app#(app(fmap(),app(app(cons(),f),t_f())),x) ->
    app#(app(cons(),app(f,x)),app(app(fmap(),t_f()),x))
    app#(app(twice(),f),x) -> app#(f,app(f,x)) ->
    app#(app(twice(),f),x) -> app#(f,x)
    app#(app(twice(),f),x) -> app#(f,app(f,x)) ->
    app#(app(twice(),f),x) -> app#(f,app(f,x))
    app#(app(twice(),f),x) -> app#(f,app(f,x)) ->
    app#(app(map(),f),app(app(cons(),h),t)) -> app#(app(map(),f),t)
    app#(app(twice(),f),x) -> app#(f,app(f,x)) ->
    app#(app(map(),f),app(app(cons(),h),t)) -> app#(f,h)
    app#(app(twice(),f),x) -> app#(f,app(f,x)) ->
    app#(app(map(),f),app(app(cons(),h),t)) -> app#(cons(),app(f,h))
    app#(app(twice(),f),x) -> app#(f,app(f,x)) ->
    app#(app(map(),f),app(app(cons(),h),t)) -> app#(app(cons(),app(f,h)),app(app(map(),f),t))
    app#(app(twice(),f),x) -> app#(f,app(f,x)) ->
    app#(app(fmap(),app(app(cons(),f),t_f())),x) -> app#(fmap(),t_f())
    app#(app(twice(),f),x) -> app#(f,app(f,x)) ->
    app#(app(fmap(),app(app(cons(),f),t_f())),x) -> app#(app(fmap(),t_f()),x)
    app#(app(twice(),f),x) -> app#(f,app(f,x)) ->
    app#(app(fmap(),app(app(cons(),f),t_f())),x) -> app#(f,x)
    app#(app(twice(),f),x) -> app#(f,app(f,x)) ->
    app#(app(fmap(),app(app(cons(),f),t_f())),x) -> app#(cons(),app(f,x))
    app#(app(twice(),f),x) -> app#(f,app(f,x)) ->
    app#(app(fmap(),app(app(cons(),f),t_f())),x) ->
    app#(app(cons(),app(f,x)),app(app(fmap(),t_f()),x))
    app#(app(twice(),f),x) -> app#(f,x) ->
    app#(app(twice(),f),x) -> app#(f,x)
    app#(app(twice(),f),x) -> app#(f,x) ->
    app#(app(twice(),f),x) -> app#(f,app(f,x))
    app#(app(twice(),f),x) -> app#(f,x) ->
    app#(app(map(),f),app(app(cons(),h),t)) -> app#(app(map(),f),t)
    app#(app(twice(),f),x) -> app#(f,x) ->
    app#(app(map(),f),app(app(cons(),h),t)) -> app#(f,h)
    app#(app(twice(),f),x) -> app#(f,x) ->
    app#(app(map(),f),app(app(cons(),h),t)) -> app#(cons(),app(f,h))
    app#(app(twice(),f),x) -> app#(f,x) ->
    app#(app(map(),f),app(app(cons(),h),t)) -> app#(app(cons(),app(f,h)),app(app(map(),f),t))
    app#(app(twice(),f),x) -> app#(f,x) ->
    app#(app(fmap(),app(app(cons(),f),t_f())),x) -> app#(fmap(),t_f())
    app#(app(twice(),f),x) -> app#(f,x) ->
    app#(app(fmap(),app(app(cons(),f),t_f())),x) -> app#(app(fmap(),t_f()),x)
    app#(app(twice(),f),x) -> app#(f,x) ->
    app#(app(fmap(),app(app(cons(),f),t_f())),x) -> app#(f,x)
    app#(app(twice(),f),x) -> app#(f,x) ->
    app#(app(fmap(),app(app(cons(),f),t_f())),x) -> app#(cons(),app(f,x))
    app#(app(twice(),f),x) -> app#(f,x) ->
    app#(app(fmap(),app(app(cons(),f),t_f())),x) ->
    app#(app(cons(),app(f,x)),app(app(fmap(),t_f()),x))
   SCC Processor:
    #sccs: 1
    #rules: 5
    #arcs: 48/121
    DPs:
     app#(app(fmap(),app(app(cons(),f),t_f())),x) -> app#(f,x)
     app#(app(map(),f),app(app(cons(),h),t)) -> app#(f,h)
     app#(app(map(),f),app(app(cons(),h),t)) -> app#(app(map(),f),t)
     app#(app(twice(),f),x) -> app#(f,app(f,x))
     app#(app(twice(),f),x) -> app#(f,x)
    TRS:
     app(app(twice(),f),x) -> app(f,app(f,x))
     app(app(map(),f),nil()) -> nil()
     app(app(map(),f),app(app(cons(),h),t)) -> app(app(cons(),app(f,h)),app(app(map(),f),t))
     app(app(fmap(),nil()),x) -> nil()
     app(app(fmap(),app(app(cons(),f),t_f())),x) ->
     app(app(cons(),app(f,x)),app(app(fmap(),t_f()),x))
    Open