- : unit = ()
- : unit = ()
h : heuristic = <heuristic>
- : unit = ()
APPLY CRITERIA (Marked dependency pairs)

TRS termination of:
[1] app(app(app(if,true),x),y) -> x
[2] app(app(app(if,true),x),y) -> y
[3] app(app(takeWhile,p),nil) -> nil
[4] app(app(takeWhile,p),app(app(cons,x),xs)) ->
 app(app(app(if,app(p,x)),app(app(cons,x),app(app(takeWhile,p),xs))),nil)
[5] app(app(dropWhile,p),nil) -> nil
[6] app(app(dropWhile,p),app(app(cons,x),xs)) ->
 app(app(app(if,app(p,x)),app(app(dropWhile,p),xs)),app(app(cons,x),xs))


Sub problem: 
guided: 

DP termination of:
<Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    if,
                                                                    app(p,x)),
                                                                app(app(cons,x),
                                                                 app(
                                                                  app(
                                                                   takeWhile,
                                                                   p),
                                                                  xs))),
                                                     nil)>
<Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(app(if,app(p,x)),
                                                     app(app(cons,x),
                                                      app(app(takeWhile,p),xs)))>
<Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(if,app(p,x))>
<Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(p,x)>
<Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(app(cons,x),
                                                     app(app(takeWhile,p),xs))>
<Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(app(takeWhile,p),
                                                     xs)>
<Marked_app(app(dropWhile,p),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    if,
                                                                    app(p,x)),
                                                                app(app(
                                                                    dropWhile,
                                                                    p),
                                                                 xs)),
                                                     app(app(cons,x),xs))>
<Marked_app(app(dropWhile,p),app(app(cons,x),xs)) , Marked_app(app(if,app(p,x)),
                                                     app(app(dropWhile,p),xs))>
<Marked_app(app(dropWhile,p),app(app(cons,x),xs)) , Marked_app(if,app(p,x))>
<Marked_app(app(dropWhile,p),app(app(cons,x),xs)) , Marked_app(p,x)>
<Marked_app(app(dropWhile,p),app(app(cons,x),xs)) , Marked_app(app(dropWhile,p),
                                                     xs)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_app(app(dropWhile,p),app(app(cons,x),xs)) , Marked_app(app(
                                                                   dropWhile,
                                                                   p),
                                                        xs)> 
      --> <Marked_app(app(dropWhile,p),app(app(cons,x),xs)) , Marked_app(
                                                               app(dropWhile,
                                                                p),xs)>
  <Marked_app(app(dropWhile,p),app(app(cons,x),xs)) , Marked_app(app(
                                                                  dropWhile,
                                                                  p),
                                                       xs)> 
     --> <Marked_app(app(dropWhile,p),app(app(cons,x),xs)) , Marked_app(p,x)>
  <Marked_app(app(dropWhile,p),app(app(cons,x),xs)) , Marked_app(app(
                                                                  dropWhile,
                                                                  p),
                                                       xs)> 
     --> <Marked_app(app(dropWhile,p),app(app(cons,x),xs)) , Marked_app(
                                                              app(if,
                                                               app(p,x)),
                                                              app(app(
                                                                   dropWhile,
                                                                   p),
                                                               xs))>
  <Marked_app(app(dropWhile,p),app(app(cons,x),xs)) , Marked_app(app(
                                                                  dropWhile,
                                                                  p),
                                                       xs)> 
     --> <Marked_app(app(dropWhile,p),app(app(cons,x),xs)) , Marked_app(
                                                              app(app(
                                                                   if,
                                                                   app(p,x)),
                                                               app(app(
                                                                    dropWhile,
                                                                    p),
                                                                xs)),
                                                              app(app(cons,x),
                                                               xs))>
  <Marked_app(app(dropWhile,p),app(app(cons,x),xs)) , Marked_app(app(
                                                                  dropWhile,
                                                                  p),
                                                       xs)> 
     --> <Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(
                                                              app(takeWhile,
                                                               p),xs)>
  <Marked_app(app(dropWhile,p),app(app(cons,x),xs)) , Marked_app(app(
                                                                  dropWhile,
                                                                  p),
                                                       xs)> 
     --> <Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(
                                                              app(cons,
                                                               x),
                                                              app(app(
                                                                   takeWhile,
                                                                   p),
                                                               xs))>
  <Marked_app(app(dropWhile,p),app(app(cons,x),xs)) , Marked_app(app(
                                                                  dropWhile,
                                                                  p),
                                                       xs)> 
     --> <Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(p,x)>
  <Marked_app(app(dropWhile,p),app(app(cons,x),xs)) , Marked_app(app(
                                                                  dropWhile,
                                                                  p),
                                                       xs)> 
     --> <Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(
                                                              app(if,
                                                               app(p,x)),
                                                              app(app(cons,x),
                                                               app(app(
                                                                    takeWhile,
                                                                    p),
                                                                xs)))>
  <Marked_app(app(dropWhile,p),app(app(cons,x),xs)) , Marked_app(p,x)> 
     --> <Marked_app(app(dropWhile,p),app(app(cons,x),xs)) , Marked_app(
                                                              app(dropWhile,
                                                               p),xs)>
  <Marked_app(app(dropWhile,p),app(app(cons,x),xs)) , Marked_app(p,x)> 
     --> <Marked_app(app(dropWhile,p),app(app(cons,x),xs)) , Marked_app(p,x)>
  <Marked_app(app(dropWhile,p),app(app(cons,x),xs)) , Marked_app(p,x)> 
     --> <Marked_app(app(dropWhile,p),app(app(cons,x),xs)) , Marked_app(
                                                              app(if,
                                                               app(p,x)),
                                                              app(app(
                                                                   dropWhile,
                                                                   p),
                                                               xs))>
  <Marked_app(app(dropWhile,p),app(app(cons,x),xs)) , Marked_app(p,x)> 
     --> <Marked_app(app(dropWhile,p),app(app(cons,x),xs)) , Marked_app(
                                                              app(app(
                                                                   if,
                                                                   app(p,x)),
                                                               app(app(
                                                                    dropWhile,
                                                                    p),
                                                                xs)),
                                                              app(app(cons,x),
                                                               xs))>
  <Marked_app(app(dropWhile,p),app(app(cons,x),xs)) , Marked_app(p,x)> 
     --> <Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(
                                                              app(takeWhile,
                                                               p),xs)>
  <Marked_app(app(dropWhile,p),app(app(cons,x),xs)) , Marked_app(p,x)> 
     --> <Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(
                                                              app(cons,
                                                               x),
                                                              app(app(
                                                                   takeWhile,
                                                                   p),
                                                               xs))>
  <Marked_app(app(dropWhile,p),app(app(cons,x),xs)) , Marked_app(p,x)> 
     --> <Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(p,x)>
  <Marked_app(app(dropWhile,p),app(app(cons,x),xs)) , Marked_app(p,x)> 
     --> <Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(
                                                              app(if,
                                                               app(p,x)),
                                                              app(app(cons,x),
                                                               app(app(
                                                                    takeWhile,
                                                                    p),
                                                                xs)))>
  <Marked_app(app(dropWhile,p),app(app(cons,x),xs)) , Marked_app(app(
                                                                  if,
                                                                  app(p,x)),
                                                       app(app(dropWhile,p),xs))> 
     --> <Marked_app(app(dropWhile,p),app(app(cons,x),xs)) , Marked_app(
                                                              app(dropWhile,
                                                               p),xs)>
  <Marked_app(app(dropWhile,p),app(app(cons,x),xs)) , Marked_app(app(
                                                                  if,
                                                                  app(p,x)),
                                                       app(app(dropWhile,p),xs))> 
     --> <Marked_app(app(dropWhile,p),app(app(cons,x),xs)) , Marked_app(p,x)>
  <Marked_app(app(dropWhile,p),app(app(cons,x),xs)) , Marked_app(app(
                                                                  if,
                                                                  app(p,x)),
                                                       app(app(dropWhile,p),xs))> 
     --> <Marked_app(app(dropWhile,p),app(app(cons,x),xs)) , Marked_app(
                                                              app(if,
                                                               app(p,x)),
                                                              app(app(
                                                                   dropWhile,
                                                                   p),
                                                               xs))>
  <Marked_app(app(dropWhile,p),app(app(cons,x),xs)) , Marked_app(app(
                                                                  if,
                                                                  app(p,x)),
                                                       app(app(dropWhile,p),xs))> 
     --> <Marked_app(app(dropWhile,p),app(app(cons,x),xs)) , Marked_app(
                                                              app(app(
                                                                   if,
                                                                   app(p,x)),
                                                               app(app(
                                                                    dropWhile,
                                                                    p),
                                                                xs)),
                                                              app(app(cons,x),
                                                               xs))>
  <Marked_app(app(dropWhile,p),app(app(cons,x),xs)) , Marked_app(app(
                                                                  if,
                                                                  app(p,x)),
                                                       app(app(dropWhile,p),xs))> 
     --> <Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(
                                                              app(takeWhile,
                                                               p),xs)>
  <Marked_app(app(dropWhile,p),app(app(cons,x),xs)) , Marked_app(app(
                                                                  if,
                                                                  app(p,x)),
                                                       app(app(dropWhile,p),xs))> 
     --> <Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(
                                                              app(cons,
                                                               x),
                                                              app(app(
                                                                   takeWhile,
                                                                   p),
                                                               xs))>
  <Marked_app(app(dropWhile,p),app(app(cons,x),xs)) , Marked_app(app(
                                                                  if,
                                                                  app(p,x)),
                                                       app(app(dropWhile,p),xs))> 
     --> <Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(p,x)>
  <Marked_app(app(dropWhile,p),app(app(cons,x),xs)) , Marked_app(app(
                                                                  if,
                                                                  app(p,x)),
                                                       app(app(dropWhile,p),xs))> 
     --> <Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(
                                                              app(if,
                                                               app(p,x)),
                                                              app(app(cons,x),
                                                               app(app(
                                                                    takeWhile,
                                                                    p),
                                                                xs)))>
  <Marked_app(app(dropWhile,p),app(app(cons,x),xs)) , Marked_app(app(
                                                                  app(
                                                                   if,
                                                                   app(p,x)),
                                                                  app(
                                                                   app(
                                                                    dropWhile,
                                                                    p),
                                                                   xs)),
                                                       app(app(cons,x),xs))> 
     --> <Marked_app(app(dropWhile,p),app(app(cons,x),xs)) , Marked_app(
                                                              app(dropWhile,
                                                               p),xs)>
  <Marked_app(app(dropWhile,p),app(app(cons,x),xs)) , Marked_app(app(
                                                                  app(
                                                                   if,
                                                                   app(p,x)),
                                                                  app(
                                                                   app(
                                                                    dropWhile,
                                                                    p),
                                                                   xs)),
                                                       app(app(cons,x),xs))> 
     --> <Marked_app(app(dropWhile,p),app(app(cons,x),xs)) , Marked_app(p,x)>
  <Marked_app(app(dropWhile,p),app(app(cons,x),xs)) , Marked_app(app(
                                                                  app(
                                                                   if,
                                                                   app(p,x)),
                                                                  app(
                                                                   app(
                                                                    dropWhile,
                                                                    p),
                                                                   xs)),
                                                       app(app(cons,x),xs))> 
     --> <Marked_app(app(dropWhile,p),app(app(cons,x),xs)) , Marked_app(
                                                              app(if,
                                                               app(p,x)),
                                                              app(app(
                                                                   dropWhile,
                                                                   p),
                                                               xs))>
  <Marked_app(app(dropWhile,p),app(app(cons,x),xs)) , Marked_app(app(
                                                                  app(
                                                                   if,
                                                                   app(p,x)),
                                                                  app(
                                                                   app(
                                                                    dropWhile,
                                                                    p),
                                                                   xs)),
                                                       app(app(cons,x),xs))> 
     --> <Marked_app(app(dropWhile,p),app(app(cons,x),xs)) , Marked_app(
                                                              app(app(
                                                                   if,
                                                                   app(p,x)),
                                                               app(app(
                                                                    dropWhile,
                                                                    p),
                                                                xs)),
                                                              app(app(cons,x),
                                                               xs))>
  <Marked_app(app(dropWhile,p),app(app(cons,x),xs)) , Marked_app(app(
                                                                  app(
                                                                   if,
                                                                   app(p,x)),
                                                                  app(
                                                                   app(
                                                                    dropWhile,
                                                                    p),
                                                                   xs)),
                                                       app(app(cons,x),xs))> 
     --> <Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(
                                                              app(takeWhile,
                                                               p),xs)>
  <Marked_app(app(dropWhile,p),app(app(cons,x),xs)) , Marked_app(app(
                                                                  app(
                                                                   if,
                                                                   app(p,x)),
                                                                  app(
                                                                   app(
                                                                    dropWhile,
                                                                    p),
                                                                   xs)),
                                                       app(app(cons,x),xs))> 
     --> <Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(
                                                              app(cons,
                                                               x),
                                                              app(app(
                                                                   takeWhile,
                                                                   p),
                                                               xs))>
  <Marked_app(app(dropWhile,p),app(app(cons,x),xs)) , Marked_app(app(
                                                                  app(
                                                                   if,
                                                                   app(p,x)),
                                                                  app(
                                                                   app(
                                                                    dropWhile,
                                                                    p),
                                                                   xs)),
                                                       app(app(cons,x),xs))> 
     --> <Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(p,x)>
  <Marked_app(app(dropWhile,p),app(app(cons,x),xs)) , Marked_app(app(
                                                                  app(
                                                                   if,
                                                                   app(p,x)),
                                                                  app(
                                                                   app(
                                                                    dropWhile,
                                                                    p),
                                                                   xs)),
                                                       app(app(cons,x),xs))> 
     --> <Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(
                                                              app(if,
                                                               app(p,x)),
                                                              app(app(cons,x),
                                                               app(app(
                                                                    takeWhile,
                                                                    p),
                                                                xs)))>
  <Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(app(
                                                                  takeWhile,
                                                                  p),
                                                       xs)> 
     --> <Marked_app(app(dropWhile,p),app(app(cons,x),xs)) , Marked_app(
                                                              app(dropWhile,
                                                               p),xs)>
  <Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(app(
                                                                  takeWhile,
                                                                  p),
                                                       xs)> 
     --> <Marked_app(app(dropWhile,p),app(app(cons,x),xs)) , Marked_app(p,x)>
  <Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(app(
                                                                  takeWhile,
                                                                  p),
                                                       xs)> 
     --> <Marked_app(app(dropWhile,p),app(app(cons,x),xs)) , Marked_app(
                                                              app(if,
                                                               app(p,x)),
                                                              app(app(
                                                                   dropWhile,
                                                                   p),
                                                               xs))>
  <Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(app(
                                                                  takeWhile,
                                                                  p),
                                                       xs)> 
     --> <Marked_app(app(dropWhile,p),app(app(cons,x),xs)) , Marked_app(
                                                              app(app(
                                                                   if,
                                                                   app(p,x)),
                                                               app(app(
                                                                    dropWhile,
                                                                    p),
                                                                xs)),
                                                              app(app(cons,x),
                                                               xs))>
  <Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(app(
                                                                  takeWhile,
                                                                  p),
                                                       xs)> 
     --> <Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(
                                                              app(takeWhile,
                                                               p),xs)>
  <Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(app(
                                                                  takeWhile,
                                                                  p),
                                                       xs)> 
     --> <Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(
                                                              app(cons,
                                                               x),
                                                              app(app(
                                                                   takeWhile,
                                                                   p),
                                                               xs))>
  <Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(app(
                                                                  takeWhile,
                                                                  p),
                                                       xs)> 
     --> <Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(p,x)>
  <Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(app(
                                                                  takeWhile,
                                                                  p),
                                                       xs)> 
     --> <Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(
                                                              app(if,
                                                               app(p,x)),
                                                              app(app(cons,x),
                                                               app(app(
                                                                    takeWhile,
                                                                    p),
                                                                xs)))>
  <Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(app(cons,x),
                                                       app(app(takeWhile,p),xs))> 
     --> <Marked_app(app(dropWhile,p),app(app(cons,x),xs)) , Marked_app(
                                                              app(dropWhile,
                                                               p),xs)>
  <Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(app(cons,x),
                                                       app(app(takeWhile,p),xs))> 
     --> <Marked_app(app(dropWhile,p),app(app(cons,x),xs)) , Marked_app(p,x)>
  <Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(app(cons,x),
                                                       app(app(takeWhile,p),xs))> 
     --> <Marked_app(app(dropWhile,p),app(app(cons,x),xs)) , Marked_app(
                                                              app(if,
                                                               app(p,x)),
                                                              app(app(
                                                                   dropWhile,
                                                                   p),
                                                               xs))>
  <Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(app(cons,x),
                                                       app(app(takeWhile,p),xs))> 
     --> <Marked_app(app(dropWhile,p),app(app(cons,x),xs)) , Marked_app(
                                                              app(app(
                                                                   if,
                                                                   app(p,x)),
                                                               app(app(
                                                                    dropWhile,
                                                                    p),
                                                                xs)),
                                                              app(app(cons,x),
                                                               xs))>
  <Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(app(cons,x),
                                                       app(app(takeWhile,p),xs))> 
     --> <Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(
                                                              app(takeWhile,
                                                               p),xs)>
  <Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(app(cons,x),
                                                       app(app(takeWhile,p),xs))> 
     --> <Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(
                                                              app(cons,
                                                               x),
                                                              app(app(
                                                                   takeWhile,
                                                                   p),
                                                               xs))>
  <Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(app(cons,x),
                                                       app(app(takeWhile,p),xs))> 
     --> <Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(p,x)>
  <Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(app(cons,x),
                                                       app(app(takeWhile,p),xs))> 
     --> <Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(
                                                              app(if,
                                                               app(p,x)),
                                                              app(app(cons,x),
                                                               app(app(
                                                                    takeWhile,
                                                                    p),
                                                                xs)))>
  <Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(p,x)> 
     --> <Marked_app(app(dropWhile,p),app(app(cons,x),xs)) , Marked_app(
                                                              app(dropWhile,
                                                               p),xs)>
  <Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(p,x)> 
     --> <Marked_app(app(dropWhile,p),app(app(cons,x),xs)) , Marked_app(p,x)>
  <Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(p,x)> 
     --> <Marked_app(app(dropWhile,p),app(app(cons,x),xs)) , Marked_app(
                                                              app(if,
                                                               app(p,x)),
                                                              app(app(
                                                                   dropWhile,
                                                                   p),
                                                               xs))>
  <Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(p,x)> 
     --> <Marked_app(app(dropWhile,p),app(app(cons,x),xs)) , Marked_app(
                                                              app(app(
                                                                   if,
                                                                   app(p,x)),
                                                               app(app(
                                                                    dropWhile,
                                                                    p),
                                                                xs)),
                                                              app(app(cons,x),
                                                               xs))>
  <Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(p,x)> 
     --> <Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(
                                                              app(takeWhile,
                                                               p),xs)>
  <Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(p,x)> 
     --> <Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(
                                                              app(cons,
                                                               x),
                                                              app(app(
                                                                   takeWhile,
                                                                   p),
                                                               xs))>
  <Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(p,x)> 
     --> <Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(p,x)>
  <Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(p,x)> 
     --> <Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(
                                                              app(if,
                                                               app(p,x)),
                                                              app(app(cons,x),
                                                               app(app(
                                                                    takeWhile,
                                                                    p),
                                                                xs)))>
  <Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(app(
                                                                  if,
                                                                  app(p,x)),
                                                       app(app(cons,x),
                                                        app(app(takeWhile,p),
                                                         xs)))> 
     --> <Marked_app(app(dropWhile,p),app(app(cons,x),xs)) , Marked_app(
                                                              app(dropWhile,
                                                               p),xs)>
  <Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(app(
                                                                  if,
                                                                  app(p,x)),
                                                       app(app(cons,x),
                                                        app(app(takeWhile,p),
                                                         xs)))> 
     --> <Marked_app(app(dropWhile,p),app(app(cons,x),xs)) , Marked_app(p,x)>
  <Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(app(
                                                                  if,
                                                                  app(p,x)),
                                                       app(app(cons,x),
                                                        app(app(takeWhile,p),
                                                         xs)))> 
     --> <Marked_app(app(dropWhile,p),app(app(cons,x),xs)) , Marked_app(
                                                              app(if,
                                                               app(p,x)),
                                                              app(app(
                                                                   dropWhile,
                                                                   p),
                                                               xs))>
  <Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(app(
                                                                  if,
                                                                  app(p,x)),
                                                       app(app(cons,x),
                                                        app(app(takeWhile,p),
                                                         xs)))> 
     --> <Marked_app(app(dropWhile,p),app(app(cons,x),xs)) , Marked_app(
                                                              app(app(
                                                                   if,
                                                                   app(p,x)),
                                                               app(app(
                                                                    dropWhile,
                                                                    p),
                                                                xs)),
                                                              app(app(cons,x),
                                                               xs))>
  <Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(app(
                                                                  if,
                                                                  app(p,x)),
                                                       app(app(cons,x),
                                                        app(app(takeWhile,p),
                                                         xs)))> 
     --> <Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(
                                                              app(takeWhile,
                                                               p),xs)>
  <Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(app(
                                                                  if,
                                                                  app(p,x)),
                                                       app(app(cons,x),
                                                        app(app(takeWhile,p),
                                                         xs)))> 
     --> <Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(
                                                              app(cons,
                                                               x),
                                                              app(app(
                                                                   takeWhile,
                                                                   p),
                                                               xs))>
  <Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(app(
                                                                  if,
                                                                  app(p,x)),
                                                       app(app(cons,x),
                                                        app(app(takeWhile,p),
                                                         xs)))> 
     --> <Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(p,x)>
  <Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(app(
                                                                  if,
                                                                  app(p,x)),
                                                       app(app(cons,x),
                                                        app(app(takeWhile,p),
                                                         xs)))> 
     --> <Marked_app(app(takeWhile,p),app(app(cons,x),xs)) , Marked_app(
                                                              app(if,
                                                               app(p,x)),
                                                              app(app(cons,x),
                                                               app(app(
                                                                    takeWhile,
                                                                    p),
                                                                xs)))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  app(app(app(if,true),x),y) >= x ;
  app(app(app(if,true),x),y) >= y ;
  app(app(takeWhile,p),app(app(cons,x),xs)) >= app(app(app(if,app(p,x)),
                                                    app(app(cons,x),
                                                     app(app(takeWhile,p),xs))),
                                                nil) ;
  app(app(takeWhile,p),nil) >= nil ;
  app(app(dropWhile,p),app(app(cons,x),xs)) >= app(app(app(if,app(p,x)),
                                                    app(app(dropWhile,p),xs)),
                                                app(app(cons,x),xs)) ;
  app(app(dropWhile,p),nil) >= nil ;
  Marked_app(app(takeWhile,p),app(app(cons,x),xs)) >= Marked_app(app(
                                                                  if,
                                                                  app(p,x)),
                                                       app(app(cons,x),
                                                        app(app(takeWhile,p),
                                                         xs))) ;
  Marked_app(app(takeWhile,p),app(app(cons,x),xs)) >= Marked_app(app(
                                                                  takeWhile,
                                                                  p),
                                                       xs) ;
  Marked_app(app(takeWhile,p),app(app(cons,x),xs)) >= Marked_app(app(cons,x),
                                                       app(app(takeWhile,p),xs)) ;
  Marked_app(app(takeWhile,p),app(app(cons,x),xs)) >= Marked_app(p,x) ;
  Marked_app(app(dropWhile,p),app(app(cons,x),xs)) >= Marked_app(app(
                                                                  app(
                                                                   if,
                                                                   app(p,x)),
                                                                  app(
                                                                   app(
                                                                    dropWhile,
                                                                    p),
                                                                   xs)),
                                                       app(app(cons,x),xs)) ;
  Marked_app(app(dropWhile,p),app(app(cons,x),xs)) >= Marked_app(app(
                                                                  if,
                                                                  app(p,x)),
                                                       app(app(dropWhile,p),xs)) ;
  Marked_app(app(dropWhile,p),app(app(cons,x),xs)) >= Marked_app(app(
                                                                  dropWhile,
                                                                  p),
                                                       xs) ;
  Marked_app(app(dropWhile,p),app(app(cons,x),xs)) >= Marked_app(p,x) ;
 }
 + Disjunctions:{ 
{
  Marked_app(app(takeWhile,p),app(app(cons,x),xs)) > Marked_app(app(if,
                                                                 app(p,x)),
                                                      app(app(cons,x),
                                                       app(app(takeWhile,p),xs)))
                                                       ;
 }
{
  Marked_app(app(takeWhile,p),app(app(cons,x),xs)) > Marked_app(app(takeWhile,
                                                                 p),xs) ;
 }
{
  Marked_app(app(takeWhile,p),app(app(cons,x),xs)) > Marked_app(app(cons,x),
                                                      app(app(takeWhile,p),xs)) ;
 }
{
  Marked_app(app(takeWhile,p),app(app(cons,x),xs)) > Marked_app(p,x) ;
 }
{
  Marked_app(app(dropWhile,p),app(app(cons,x),xs)) > Marked_app(app(app(
                                                                    if,
                                                                    app(p,x)),
                                                                 app(
                                                                  app(
                                                                   dropWhile,
                                                                   p),
                                                                  xs)),
                                                      app(app(cons,x),xs)) ;
 }
{
  Marked_app(app(dropWhile,p),app(app(cons,x),xs)) > Marked_app(app(if,
                                                                 app(p,x)),
                                                      app(app(dropWhile,p),xs)) ;
 }
{
  Marked_app(app(dropWhile,p),app(app(cons,x),xs)) > Marked_app(app(dropWhile,
                                                                 p),xs) ;
 }
{
  Marked_app(app(dropWhile,p),app(app(cons,x),xs)) > Marked_app(p,x) ;
 }
 } 
=== TIMER virtual : 10.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 10.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
Entering rpo_solver
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 15.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 15.000000 ===
=== STOPING TIMER real ===
Sat timeout reached
=== STOPING TIMER virtual ===
Time out for these parameters.
=== TIMER virtual : 50.000000 ===
trying sub matrices of size: 1
Matrix interpretation constraints generated.
Search parameters: LINEAR MATRIX 3x3 (strict=1x1) ; time limit: 50.. 
Termination constraints generated.
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 50.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
No solution found for these constraints.
APPLY CRITERIA (Simple graph)
Found the following constraints:
{
  app(app(app(if,true),x),y) >= x ;
  app(app(app(if,true),x),y) >= y ;
  app(app(takeWhile,p),app(app(cons,x),xs)) >= app(app(app(if,app(p,x)),
                                                    app(app(cons,x),
                                                     app(app(takeWhile,p),xs))),
                                                nil) ;
  app(app(takeWhile,p),nil) >= nil ;
  app(app(dropWhile,p),app(app(cons,x),xs)) >= app(app(app(if,app(p,x)),
                                                    app(app(dropWhile,p),xs)),
                                                app(app(cons,x),xs)) ;
  app(app(dropWhile,p),nil) >= nil ;
  Marked_app(app(takeWhile,p),app(app(cons,x),xs)) > Marked_app(app(if,
                                                                 app(p,x)),
                                                      app(app(cons,x),
                                                       app(app(takeWhile,p),xs)))
                                                       ;
  Marked_app(app(takeWhile,p),app(app(cons,x),xs)) > Marked_app(app(takeWhile,
                                                                 p),xs) ;
  Marked_app(app(takeWhile,p),app(app(cons,x),xs)) > Marked_app(app(cons,x),
                                                      app(app(takeWhile,p),xs)) ;
  Marked_app(app(takeWhile,p),app(app(cons,x),xs)) > Marked_app(p,x) ;
  Marked_app(app(dropWhile,p),app(app(cons,x),xs)) > Marked_app(app(app(
                                                                    if,
                                                                    app(p,x)),
                                                                 app(
                                                                  app(
                                                                   dropWhile,
                                                                   p),
                                                                  xs)),
                                                      app(app(cons,x),xs)) ;
  Marked_app(app(dropWhile,p),app(app(cons,x),xs)) > Marked_app(app(if,
                                                                 app(p,x)),
                                                      app(app(dropWhile,p),xs)) ;
  Marked_app(app(dropWhile,p),app(app(cons,x),xs)) > Marked_app(app(dropWhile,
                                                                 p),xs) ;
  Marked_app(app(dropWhile,p),app(app(cons,x),xs)) > Marked_app(p,x) ;
 }

APPLY CRITERIA (SOLVE_ORD)
Trying to solve the following constraints:
{
  app(app(app(if,true),x),y) >= x ;
  app(app(app(if,true),x),y) >= y ;
  app(app(takeWhile,p),app(app(cons,x),xs)) >= app(app(app(if,app(p,x)),
                                                    app(app(cons,x),
                                                     app(app(takeWhile,p),xs))),
                                                nil) ;
  app(app(takeWhile,p),nil) >= nil ;
  app(app(dropWhile,p),app(app(cons,x),xs)) >= app(app(app(if,app(p,x)),
                                                    app(app(dropWhile,p),xs)),
                                                app(app(cons,x),xs)) ;
  app(app(dropWhile,p),nil) >= nil ;
  Marked_app(app(takeWhile,p),app(app(cons,x),xs)) > Marked_app(app(if,
                                                                 app(p,x)),
                                                      app(app(cons,x),
                                                       app(app(takeWhile,p),xs)))
                                                       ;
  Marked_app(app(takeWhile,p),app(app(cons,x),xs)) > Marked_app(app(takeWhile,
                                                                 p),xs) ;
  Marked_app(app(takeWhile,p),app(app(cons,x),xs)) > Marked_app(app(cons,x),
                                                      app(app(takeWhile,p),xs)) ;
  Marked_app(app(takeWhile,p),app(app(cons,x),xs)) > Marked_app(p,x) ;
  Marked_app(app(dropWhile,p),app(app(cons,x),xs)) > Marked_app(app(app(
                                                                    if,
                                                                    app(p,x)),
                                                                 app(
                                                                  app(
                                                                   dropWhile,
                                                                   p),
                                                                  xs)),
                                                      app(app(cons,x),xs)) ;
  Marked_app(app(dropWhile,p),app(app(cons,x),xs)) > Marked_app(app(if,
                                                                 app(p,x)),
                                                      app(app(dropWhile,p),xs)) ;
  Marked_app(app(dropWhile,p),app(app(cons,x),xs)) > Marked_app(app(dropWhile,
                                                                 p),xs) ;
  Marked_app(app(dropWhile,p),app(app(cons,x),xs)) > Marked_app(p,x) ;
 }
 + Disjunctions:{ 
 } 
=== TIMER virtual : 10.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 10.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
Entering rpo_solver
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
No solution found for these parameters.(6 bt (0) [8])
=== TIMER virtual : 15.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 15.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
=== TIMER virtual : 50.000000 ===
trying sub matrices of size: 1
Matrix interpretation constraints generated.
Search parameters: LINEAR MATRIX 3x3 (strict=1x1) ; time limit: 50.. 
Termination constraints generated.
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 50.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
No solution found for these constraints.
APPLY CRITERIA (ID_CRIT)
NOT SOLVED
No proof found
Cime worked for 89.778209 seconds (real time)
Cime Exit Status: 0