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))
  EDG 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))
   graph:
    app#(app(maptlist(),f),app(app(cons(),x),xs)) -> 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#(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(maptlist(),f),xs) ->
    app#(app(maptlist(),f),app(app(cons(),x),xs)) -> app#(app(mapt(),f),x)
    app#(app(maptlist(),f),app(app(cons(),x),xs)) -> app#(app(maptlist(),f),xs) ->
    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(maptlist(),f),xs) ->
    app#(app(maptlist(),f),app(app(cons(),x),xs)) ->
    app#(app(cons(),app(app(mapt(),f),x)),app(app(maptlist(),f),xs))
    app#(app(maptlist(),f),app(app(cons(),x),xs)) -> app#(app(mapt(),f),x) ->
    app#(app(mapt(),f),app(leaf(),x)) -> app#(f,x)
    app#(app(maptlist(),f),app(app(cons(),x),xs)) -> app#(app(mapt(),f),x) ->
    app#(app(mapt(),f),app(leaf(),x)) -> app#(leaf(),app(f,x))
    app#(app(maptlist(),f),app(app(cons(),x),xs)) -> app#(app(mapt(),f),x) ->
    app#(app(mapt(),f),app(node(),xs)) -> app#(maptlist(),f)
    app#(app(maptlist(),f),app(app(cons(),x),xs)) -> app#(app(mapt(),f),x) ->
    app#(app(mapt(),f),app(node(),xs)) -> app#(app(maptlist(),f),xs)
    app#(app(maptlist(),f),app(app(cons(),x),xs)) -> app#(app(mapt(),f),x) ->
    app#(app(mapt(),f),app(node(),xs)) -> app#(node(),app(app(maptlist(),f),xs))
    app#(app(mapt(),f),app(node(),xs)) -> app#(app(maptlist(),f),xs) ->
    app#(app(maptlist(),f),app(app(cons(),x),xs)) -> app#(app(maptlist(),f),xs)
    app#(app(mapt(),f),app(node(),xs)) -> app#(app(maptlist(),f),xs) ->
    app#(app(maptlist(),f),app(app(cons(),x),xs)) -> app#(mapt(),f)
    app#(app(mapt(),f),app(node(),xs)) -> app#(app(maptlist(),f),xs) ->
    app#(app(maptlist(),f),app(app(cons(),x),xs)) -> app#(app(mapt(),f),x)
    app#(app(mapt(),f),app(node(),xs)) -> app#(app(maptlist(),f),xs) ->
    app#(app(maptlist(),f),app(app(cons(),x),xs)) -> app#(cons(),app(app(mapt(),f),x))
    app#(app(mapt(),f),app(node(),xs)) -> app#(app(maptlist(),f),xs) ->
    app#(app(maptlist(),f),app(app(cons(),x),xs)) ->
    app#(app(cons(),app(app(mapt(),f),x)),app(app(maptlist(),f),xs))
    app#(app(mapt(),f),app(leaf(),x)) -> app#(f,x) ->
    app#(app(mapt(),f),app(leaf(),x)) -> app#(f,x)
    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(leaf(),x)) -> app#(f,x) ->
    app#(app(mapt(),f),app(node(),xs)) -> app#(maptlist(),f)
    app#(app(mapt(),f),app(leaf(),x)) -> app#(f,x) ->
    app#(app(mapt(),f),app(node(),xs)) -> app#(app(maptlist(),f),xs)
    app#(app(mapt(),f),app(leaf(),x)) -> app#(f,x) ->
    app#(app(mapt(),f),app(node(),xs)) -> app#(node(),app(app(maptlist(),f),xs))
    app#(app(mapt(),f),app(leaf(),x)) -> app#(f,x) ->
    app#(app(maptlist(),f),app(app(cons(),x),xs)) -> app#(app(maptlist(),f),xs)
    app#(app(mapt(),f),app(leaf(),x)) -> app#(f,x) ->
    app#(app(maptlist(),f),app(app(cons(),x),xs)) -> app#(mapt(),f)
    app#(app(mapt(),f),app(leaf(),x)) -> app#(f,x) ->
    app#(app(maptlist(),f),app(app(cons(),x),xs)) -> app#(app(mapt(),f),x)
    app#(app(mapt(),f),app(leaf(),x)) -> app#(f,x) ->
    app#(app(maptlist(),f),app(app(cons(),x),xs)) -> app#(cons(),app(app(mapt(),f),x))
    app#(app(mapt(),f),app(leaf(),x)) -> app#(f,x) ->
    app#(app(maptlist(),f),app(app(cons(),x),xs)) ->
    app#(app(cons(),app(app(mapt(),f),x)),app(app(maptlist(),f),xs))
   Restore Modifier:
    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))
    SCC Processor:
     #sccs: 1
     #rules: 4
     #arcs: 25/100
     DPs:
      app#(app(maptlist(),f),app(app(cons(),x),xs)) -> app#(app(maptlist(),f),xs)
      app#(app(maptlist(),f),app(app(cons(),x),xs)) -> app#(app(mapt(),f),x)
      app#(app(mapt(),f),app(node(),xs)) -> app#(app(maptlist(),f),xs)
      app#(app(mapt(),f),app(leaf(),x)) -> app#(f,x)
     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))
     Matrix Interpretation Processor:
      dimension: 1
      interpretation:
       [app#](x0, x1) = x0,
       
       [cons] = 0,
       
       [nil] = 1,
       
       [maptlist] = 0,
       
       [node] = 0,
       
       [leaf] = 0,
       
       [app](x0, x1) = x1 + 1,
       
       [mapt] = 0
      orientation:
       app#(app(maptlist(),f),app(app(cons(),x),xs)) = f + 1 >= f + 1 = app#(app(maptlist(),f),xs)
       
       app#(app(maptlist(),f),app(app(cons(),x),xs)) = f + 1 >= f + 1 = app#(app(mapt(),f),x)
       
       app#(app(mapt(),f),app(node(),xs)) = f + 1 >= f + 1 = app#(app(maptlist(),f),xs)
       
       app#(app(mapt(),f),app(leaf(),x)) = f + 1 >= f = app#(f,x)
       
       app(app(mapt(),f),app(leaf(),x)) = x + 2 >= x + 2 = app(leaf(),app(f,x))
       
       app(app(mapt(),f),app(node(),xs)) = xs + 2 >= xs + 2 = app(node(),app(app(maptlist(),f),xs))
       
       app(app(maptlist(),f),nil()) = 2 >= 1 = nil()
       
       app(app(maptlist(),f),app(app(cons(),x),xs)) = xs + 2 >= xs + 2 = app(app(cons(),app(app(mapt(),f),x)),app(app(maptlist(),f),xs))
      problem:
       DPs:
        app#(app(maptlist(),f),app(app(cons(),x),xs)) -> app#(app(maptlist(),f),xs)
        app#(app(maptlist(),f),app(app(cons(),x),xs)) -> app#(app(mapt(),f),x)
        app#(app(mapt(),f),app(node(),xs)) -> 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