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(flatten(),app(app(node(),x),xs)) ->
 app(app(cons(),x),app(concat(),app(app(map(),flatten()),xs)))
 app(concat(),nil()) -> nil()
 app(concat(),app(app(cons(),x),xs)) -> app(app(append(),x),app(concat(),xs))
 app(app(append(),nil()),xs) -> xs
 app(app(append(),app(app(cons(),x),xs)),ys) -> app(app(cons(),x),app(app(append(),xs),ys))

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#(flatten(),app(app(node(),x),xs)) -> app#(map(),flatten())
   app#(flatten(),app(app(node(),x),xs)) -> app#(app(map(),flatten()),xs)
   app#(flatten(),app(app(node(),x),xs)) -> app#(concat(),app(app(map(),flatten()),xs))
   app#(flatten(),app(app(node(),x),xs)) -> app#(cons(),x)
   app#(flatten(),app(app(node(),x),xs)) ->
   app#(app(cons(),x),app(concat(),app(app(map(),flatten()),xs)))
   app#(concat(),app(app(cons(),x),xs)) -> app#(concat(),xs)
   app#(concat(),app(app(cons(),x),xs)) -> app#(append(),x)
   app#(concat(),app(app(cons(),x),xs)) -> app#(app(append(),x),app(concat(),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))
  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(flatten(),app(app(node(),x),xs)) ->
   app(app(cons(),x),app(concat(),app(app(map(),flatten()),xs)))
   app(concat(),nil()) -> nil()
   app(concat(),app(app(cons(),x),xs)) -> app(app(append(),x),app(concat(),xs))
   app(app(append(),nil()),xs) -> xs
   app(app(append(),app(app(cons(),x),xs)),ys) -> app(app(cons(),x),app(app(append(),xs),ys))
  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))
    app#(flatten(),app(app(node(),x),xs)) -> app#(map(),flatten())
    app#(flatten(),app(app(node(),x),xs)) -> app#(app(map(),flatten()),xs)
    app#(flatten(),app(app(node(),x),xs)) -> app#(concat(),app(app(map(),flatten()),xs))
    app#(flatten(),app(app(node(),x),xs)) -> app#(cons(),x)
    app#(flatten(),app(app(node(),x),xs)) ->
    app#(app(cons(),x),app(concat(),app(app(map(),flatten()),xs)))
    app#(concat(),app(app(cons(),x),xs)) -> app#(concat(),xs)
    app#(concat(),app(app(cons(),x),xs)) -> app#(append(),x)
    app#(concat(),app(app(cons(),x),xs)) -> app#(app(append(),x),app(concat(),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))
   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(flatten(),app(app(node(),x),xs)) ->
    app(app(cons(),x),app(concat(),app(app(map(),flatten()),xs)))
    app(concat(),nil()) -> nil()
    app(concat(),app(app(cons(),x),xs)) -> app(app(append(),x),app(concat(),xs))
    app(app(append(),nil()),xs) -> xs
    app(app(append(),app(app(cons(),x),xs)),ys) -> app(app(cons(),x),app(app(append(),xs),ys))
   graph:
    app#(concat(),app(app(cons(),x),xs)) -> app#(concat(),xs) ->
    app#(concat(),app(app(cons(),x),xs)) -> app#(concat(),xs)
    app#(concat(),app(app(cons(),x),xs)) -> app#(concat(),xs) ->
    app#(concat(),app(app(cons(),x),xs)) -> app#(append(),x)
    app#(concat(),app(app(cons(),x),xs)) -> app#(concat(),xs) ->
    app#(concat(),app(app(cons(),x),xs)) -> app#(app(append(),x),app(concat(),xs))
    app#(concat(),app(app(cons(),x),xs)) -> app#(app(append(),x),app(concat(),xs)) ->
    app#(app(append(),app(app(cons(),x),xs)),ys) -> app#(append(),xs)
    app#(concat(),app(app(cons(),x),xs)) -> app#(app(append(),x),app(concat(),xs)) ->
    app#(app(append(),app(app(cons(),x),xs)),ys) -> app#(app(append(),xs),ys)
    app#(concat(),app(app(cons(),x),xs)) -> app#(app(append(),x),app(concat(),xs)) ->
    app#(app(append(),app(app(cons(),x),xs)),ys) -> app#(app(cons(),x),app(app(append(),xs),ys))
    app#(flatten(),app(app(node(),x),xs)) -> app#(concat(),app(app(map(),flatten()),xs)) ->
    app#(concat(),app(app(cons(),x),xs)) -> app#(concat(),xs)
    app#(flatten(),app(app(node(),x),xs)) -> app#(concat(),app(app(map(),flatten()),xs)) ->
    app#(concat(),app(app(cons(),x),xs)) -> app#(append(),x)
    app#(flatten(),app(app(node(),x),xs)) -> app#(concat(),app(app(map(),flatten()),xs)) ->
    app#(concat(),app(app(cons(),x),xs)) -> app#(app(append(),x),app(concat(),xs))
    app#(flatten(),app(app(node(),x),xs)) -> app#(app(map(),flatten()),xs) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs)
    app#(flatten(),app(app(node(),x),xs)) -> app#(app(map(),flatten()),xs) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x)
    app#(flatten(),app(app(node(),x),xs)) -> app#(app(map(),flatten()),xs) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(cons(),app(f,x))
    app#(flatten(),app(app(node(),x),xs)) -> app#(app(map(),flatten()),xs) ->
    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#(app(append(),xs),ys) ->
    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(append(),xs),ys)
    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(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))
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(flatten(),app(app(node(),x),xs)) -> app#(map(),flatten())
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(flatten(),app(app(node(),x),xs)) -> app#(app(map(),flatten()),xs)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(flatten(),app(app(node(),x),xs)) -> app#(concat(),app(app(map(),flatten()),xs))
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(flatten(),app(app(node(),x),xs)) -> app#(cons(),x)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(flatten(),app(app(node(),x),xs)) ->
    app#(app(cons(),x),app(concat(),app(app(map(),flatten()),xs)))
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(concat(),app(app(cons(),x),xs)) -> app#(concat(),xs)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(concat(),app(app(cons(),x),xs)) -> app#(append(),x)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(concat(),app(app(cons(),x),xs)) -> app#(app(append(),x),app(concat(),xs))
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(append(),app(app(cons(),x),xs)),ys) -> app#(append(),xs)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(append(),app(app(cons(),x),xs)),ys) -> app#(app(append(),xs),ys)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(append(),app(app(cons(),x),xs)),ys) -> app#(app(cons(),x),app(app(append(),xs),ys))
   SCC Processor:
    #sccs: 3
    #rules: 5
    #arcs: 35/225
    DPs:
     app#(flatten(),app(app(node(),x),xs)) -> app#(app(map(),flatten()),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)
    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(flatten(),app(app(node(),x),xs)) ->
     app(app(cons(),x),app(concat(),app(app(map(),flatten()),xs)))
     app(concat(),nil()) -> nil()
     app(concat(),app(app(cons(),x),xs)) -> app(app(append(),x),app(concat(),xs))
     app(app(append(),nil()),xs) -> xs
     app(app(append(),app(app(cons(),x),xs)),ys) -> app(app(cons(),x),app(app(append(),xs),ys))
    Subterm Criterion Processor:
     simple projection:
      pi(app#) = 1
     problem:
      DPs:
       
      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(flatten(),app(app(node(),x),xs)) ->
       app(app(cons(),x),app(concat(),app(app(map(),flatten()),xs)))
       app(concat(),nil()) -> nil()
       app(concat(),app(app(cons(),x),xs)) -> app(app(append(),x),app(concat(),xs))
       app(app(append(),nil()),xs) -> xs
       app(app(append(),app(app(cons(),x),xs)),ys) -> app(app(cons(),x),app(app(append(),xs),ys))
     Qed
    
    DPs:
     app#(concat(),app(app(cons(),x),xs)) -> app#(concat(),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(flatten(),app(app(node(),x),xs)) ->
     app(app(cons(),x),app(concat(),app(app(map(),flatten()),xs)))
     app(concat(),nil()) -> nil()
     app(concat(),app(app(cons(),x),xs)) -> app(app(append(),x),app(concat(),xs))
     app(app(append(),nil()),xs) -> xs
     app(app(append(),app(app(cons(),x),xs)),ys) -> app(app(cons(),x),app(app(append(),xs),ys))
    Subterm Criterion Processor:
     simple projection:
      pi(app#) = 1
     problem:
      DPs:
       
      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(flatten(),app(app(node(),x),xs)) ->
       app(app(cons(),x),app(concat(),app(app(map(),flatten()),xs)))
       app(concat(),nil()) -> nil()
       app(concat(),app(app(cons(),x),xs)) -> app(app(append(),x),app(concat(),xs))
       app(app(append(),nil()),xs) -> xs
       app(app(append(),app(app(cons(),x),xs)),ys) -> app(app(cons(),x),app(app(append(),xs),ys))
     Qed
    
    DPs:
     app#(app(append(),app(app(cons(),x),xs)),ys) -> app#(app(append(),xs),ys)
    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(flatten(),app(app(node(),x),xs)) ->
     app(app(cons(),x),app(concat(),app(app(map(),flatten()),xs)))
     app(concat(),nil()) -> nil()
     app(concat(),app(app(cons(),x),xs)) -> app(app(append(),x),app(concat(),xs))
     app(app(append(),nil()),xs) -> xs
     app(app(append(),app(app(cons(),x),xs)),ys) -> app(app(cons(),x),app(app(append(),xs),ys))
    Open