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

TRS termination of:
[1] a(a(append,nil),ys) -> ys
[2] a(a(append,a(a(cons,x),xs)),ys) -> a(a(cons,x),a(a(append,xs),ys))
[3] a(a(filter,f),nil) -> nil
[4] a(a(filter,f),a(a(cons,x),xs)) -> a(a(a(if,a(f,x)),x),a(a(filter,f),xs))
[5] a(a(le,0),y) -> true
[6] a(a(le,a(s,x)),0) -> false
[7] a(a(le,a(s,x)),a(s,y)) -> a(a(le,x),y)
[8] a(a(a(if,true),x),xs) -> a(a(cons,x),xs)
[9] a(a(a(if,false),x),xs) -> xs
[10] a(a(not,f),b) -> a(not2,a(f,b))
[11] a(not2,true) -> false
[12] a(not2,false) -> true
[13] a(qs,nil) -> nil
[14] a(qs,a(a(cons,x),xs)) ->
 a(a(append,a(qs,a(a(filter,a(le,x)),xs))),
  a(a(cons,x),a(qs,a(a(filter,a(not,a(le,x))),xs))))


Sub problem: 
guided: 

DP termination of:
<Marked_a(a(append,a(a(cons,x),xs)),ys) , Marked_a(a(cons,x),
                                           a(a(append,xs),ys))>
<Marked_a(a(append,a(a(cons,x),xs)),ys) , Marked_a(a(append,xs),ys)>
<Marked_a(a(append,a(a(cons,x),xs)),ys) , Marked_a(append,xs)>
<Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(a(if,a(f,x)),x),
                                          a(a(filter,f),xs))>
<Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(if,a(f,x)),x)>
<Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(if,a(f,x))>
<Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(f,x)>
<Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(filter,f),xs)>
<Marked_a(a(le,a(s,x)),a(s,y)) , Marked_a(a(le,x),y)>
<Marked_a(a(le,a(s,x)),a(s,y)) , Marked_a(le,x)>
<Marked_a(a(a(if,true),x),xs) , Marked_a(a(cons,x),xs)>
<Marked_a(a(a(if,true),x),xs) , Marked_a(cons,x)>
<Marked_a(a(not,f),b) , Marked_a(not2,a(f,b))>
<Marked_a(a(not,f),b) , Marked_a(f,b)>
<Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(append,
                                          a(qs,a(a(filter,a(le,x)),xs))),
                                 a(a(cons,x),
                                  a(qs,a(a(filter,a(not,a(le,x))),xs))))>
<Marked_a(qs,a(a(cons,x),xs)) , Marked_a(append,a(qs,a(a(filter,a(le,x)),xs)))>
<Marked_a(qs,a(a(cons,x),xs)) , Marked_a(qs,a(a(filter,a(le,x)),xs))>
<Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(filter,a(le,x)),xs)>
<Marked_a(qs,a(a(cons,x),xs)) , Marked_a(filter,a(le,x))>
<Marked_a(qs,a(a(cons,x),xs)) , Marked_a(le,x)>
<Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(cons,x),
                                 a(qs,a(a(filter,a(not,a(le,x))),xs)))>
<Marked_a(qs,a(a(cons,x),xs)) , Marked_a(qs,a(a(filter,a(not,a(le,x))),xs))>
<Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(filter,a(not,a(le,x))),xs)>
<Marked_a(qs,a(a(cons,x),xs)) , Marked_a(filter,a(not,a(le,x)))>
<Marked_a(qs,a(a(cons,x),xs)) , Marked_a(not,a(le,x))>
<Marked_a(qs,a(a(cons,x),xs)) , Marked_a(le,x)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(filter,a(not,a(le,x))),xs)> 
      --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(filter,a(not,a(le,x))),xs)>
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(filter,a(not,a(le,x))),xs)> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(qs,
                                          a(a(filter,a(not,a(le,x))),xs))>
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(filter,a(not,a(le,x))),xs)> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(cons,x),
                                          a(qs,a(a(filter,a(not,a(le,x))),xs)))>
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(filter,a(not,a(le,x))),xs)> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(filter,a(le,x)),xs)>
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(filter,a(not,a(le,x))),xs)> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(qs,a(a(filter,a(le,x)),xs))>
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(filter,a(not,a(le,x))),xs)> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(append,
                                                   a(qs,
                                                    a(a(filter,a(le,x)),xs))),
                                          a(a(cons,x),
                                           a(qs,a(a(filter,a(not,a(le,x))),xs))))
                                          >
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(filter,a(not,a(le,x))),xs)> 
     --> <Marked_a(a(not,f),b) , Marked_a(f,b)>
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(filter,a(not,a(le,x))),xs)> 
     --> <Marked_a(a(a(if,true),x),xs) , Marked_a(a(cons,x),xs)>
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(filter,a(not,a(le,x))),xs)> 
     --> <Marked_a(a(le,a(s,x)),a(s,y)) , Marked_a(a(le,x),y)>
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(filter,a(not,a(le,x))),xs)> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(filter,f),xs)>
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(filter,a(not,a(le,x))),xs)> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(f,x)>
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(filter,a(not,a(le,x))),xs)> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(if,a(f,x)),x)>
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(filter,a(not,a(le,x))),xs)> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(a(if,a(f,x)),x),
                                                   a(a(filter,f),xs))>
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(filter,a(not,a(le,x))),xs)> 
     --> <Marked_a(a(append,a(a(cons,x),xs)),ys) , Marked_a(a(append,xs),ys)>
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(filter,a(not,a(le,x))),xs)> 
     --> <Marked_a(a(append,a(a(cons,x),xs)),ys) , Marked_a(a(cons,x),
                                                    a(a(append,xs),ys))>
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(qs,a(a(filter,a(not,a(le,x))),xs))> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(filter,a(not,a(le,x))),xs)>
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(qs,a(a(filter,a(not,a(le,x))),xs))> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(qs,
                                          a(a(filter,a(not,a(le,x))),xs))>
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(qs,a(a(filter,a(not,a(le,x))),xs))> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(cons,x),
                                          a(qs,a(a(filter,a(not,a(le,x))),xs)))>
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(qs,a(a(filter,a(not,a(le,x))),xs))> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(filter,a(le,x)),xs)>
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(qs,a(a(filter,a(not,a(le,x))),xs))> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(qs,a(a(filter,a(le,x)),xs))>
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(qs,a(a(filter,a(not,a(le,x))),xs))> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(append,
                                                   a(qs,
                                                    a(a(filter,a(le,x)),xs))),
                                          a(a(cons,x),
                                           a(qs,a(a(filter,a(not,a(le,x))),xs))))
                                          >
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(cons,x),
                                   a(qs,a(a(filter,a(not,a(le,x))),xs)))> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(filter,a(not,a(le,x))),xs)>
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(cons,x),
                                   a(qs,a(a(filter,a(not,a(le,x))),xs)))> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(qs,
                                          a(a(filter,a(not,a(le,x))),xs))>
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(cons,x),
                                   a(qs,a(a(filter,a(not,a(le,x))),xs)))> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(cons,x),
                                          a(qs,a(a(filter,a(not,a(le,x))),xs)))>
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(cons,x),
                                   a(qs,a(a(filter,a(not,a(le,x))),xs)))> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(filter,a(le,x)),xs)>
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(cons,x),
                                   a(qs,a(a(filter,a(not,a(le,x))),xs)))> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(qs,a(a(filter,a(le,x)),xs))>
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(cons,x),
                                   a(qs,a(a(filter,a(not,a(le,x))),xs)))> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(append,
                                                   a(qs,
                                                    a(a(filter,a(le,x)),xs))),
                                          a(a(cons,x),
                                           a(qs,a(a(filter,a(not,a(le,x))),xs))))
                                          >
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(cons,x),
                                   a(qs,a(a(filter,a(not,a(le,x))),xs)))> 
     --> <Marked_a(a(not,f),b) , Marked_a(f,b)>
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(cons,x),
                                   a(qs,a(a(filter,a(not,a(le,x))),xs)))> 
     --> <Marked_a(a(a(if,true),x),xs) , Marked_a(a(cons,x),xs)>
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(cons,x),
                                   a(qs,a(a(filter,a(not,a(le,x))),xs)))> 
     --> <Marked_a(a(le,a(s,x)),a(s,y)) , Marked_a(a(le,x),y)>
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(cons,x),
                                   a(qs,a(a(filter,a(not,a(le,x))),xs)))> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(filter,f),xs)>
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(cons,x),
                                   a(qs,a(a(filter,a(not,a(le,x))),xs)))> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(f,x)>
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(cons,x),
                                   a(qs,a(a(filter,a(not,a(le,x))),xs)))> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(if,a(f,x)),x)>
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(cons,x),
                                   a(qs,a(a(filter,a(not,a(le,x))),xs)))> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(a(if,a(f,x)),x),
                                                   a(a(filter,f),xs))>
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(cons,x),
                                   a(qs,a(a(filter,a(not,a(le,x))),xs)))> 
     --> <Marked_a(a(append,a(a(cons,x),xs)),ys) , Marked_a(a(append,xs),ys)>
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(cons,x),
                                   a(qs,a(a(filter,a(not,a(le,x))),xs)))> 
     --> <Marked_a(a(append,a(a(cons,x),xs)),ys) , Marked_a(a(cons,x),
                                                    a(a(append,xs),ys))>
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(filter,a(le,x)),xs)> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(filter,a(not,a(le,x))),xs)>
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(filter,a(le,x)),xs)> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(qs,
                                          a(a(filter,a(not,a(le,x))),xs))>
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(filter,a(le,x)),xs)> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(cons,x),
                                          a(qs,a(a(filter,a(not,a(le,x))),xs)))>
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(filter,a(le,x)),xs)> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(filter,a(le,x)),xs)>
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(filter,a(le,x)),xs)> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(qs,a(a(filter,a(le,x)),xs))>
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(filter,a(le,x)),xs)> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(append,
                                                   a(qs,
                                                    a(a(filter,a(le,x)),xs))),
                                          a(a(cons,x),
                                           a(qs,a(a(filter,a(not,a(le,x))),xs))))
                                          >
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(filter,a(le,x)),xs)> 
     --> <Marked_a(a(not,f),b) , Marked_a(f,b)>
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(filter,a(le,x)),xs)> 
     --> <Marked_a(a(a(if,true),x),xs) , Marked_a(a(cons,x),xs)>
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(filter,a(le,x)),xs)> 
     --> <Marked_a(a(le,a(s,x)),a(s,y)) , Marked_a(a(le,x),y)>
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(filter,a(le,x)),xs)> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(filter,f),xs)>
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(filter,a(le,x)),xs)> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(f,x)>
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(filter,a(le,x)),xs)> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(if,a(f,x)),x)>
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(filter,a(le,x)),xs)> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(a(if,a(f,x)),x),
                                                   a(a(filter,f),xs))>
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(filter,a(le,x)),xs)> 
     --> <Marked_a(a(append,a(a(cons,x),xs)),ys) , Marked_a(a(append,xs),ys)>
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(filter,a(le,x)),xs)> 
     --> <Marked_a(a(append,a(a(cons,x),xs)),ys) , Marked_a(a(cons,x),
                                                    a(a(append,xs),ys))>
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(qs,a(a(filter,a(le,x)),xs))> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(filter,a(not,a(le,x))),xs)>
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(qs,a(a(filter,a(le,x)),xs))> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(qs,
                                          a(a(filter,a(not,a(le,x))),xs))>
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(qs,a(a(filter,a(le,x)),xs))> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(cons,x),
                                          a(qs,a(a(filter,a(not,a(le,x))),xs)))>
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(qs,a(a(filter,a(le,x)),xs))> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(filter,a(le,x)),xs)>
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(qs,a(a(filter,a(le,x)),xs))> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(qs,a(a(filter,a(le,x)),xs))>
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(qs,a(a(filter,a(le,x)),xs))> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(append,
                                                   a(qs,
                                                    a(a(filter,a(le,x)),xs))),
                                          a(a(cons,x),
                                           a(qs,a(a(filter,a(not,a(le,x))),xs))))
                                          >
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(append,
                                            a(qs,a(a(filter,a(le,x)),xs))),
                                   a(a(cons,x),
                                    a(qs,a(a(filter,a(not,a(le,x))),xs))))> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(filter,a(not,a(le,x))),xs)>
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(append,
                                            a(qs,a(a(filter,a(le,x)),xs))),
                                   a(a(cons,x),
                                    a(qs,a(a(filter,a(not,a(le,x))),xs))))> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(qs,
                                          a(a(filter,a(not,a(le,x))),xs))>
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(append,
                                            a(qs,a(a(filter,a(le,x)),xs))),
                                   a(a(cons,x),
                                    a(qs,a(a(filter,a(not,a(le,x))),xs))))> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(cons,x),
                                          a(qs,a(a(filter,a(not,a(le,x))),xs)))>
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(append,
                                            a(qs,a(a(filter,a(le,x)),xs))),
                                   a(a(cons,x),
                                    a(qs,a(a(filter,a(not,a(le,x))),xs))))> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(filter,a(le,x)),xs)>
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(append,
                                            a(qs,a(a(filter,a(le,x)),xs))),
                                   a(a(cons,x),
                                    a(qs,a(a(filter,a(not,a(le,x))),xs))))> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(qs,a(a(filter,a(le,x)),xs))>
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(append,
                                            a(qs,a(a(filter,a(le,x)),xs))),
                                   a(a(cons,x),
                                    a(qs,a(a(filter,a(not,a(le,x))),xs))))> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(append,
                                                   a(qs,
                                                    a(a(filter,a(le,x)),xs))),
                                          a(a(cons,x),
                                           a(qs,a(a(filter,a(not,a(le,x))),xs))))
                                          >
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(append,
                                            a(qs,a(a(filter,a(le,x)),xs))),
                                   a(a(cons,x),
                                    a(qs,a(a(filter,a(not,a(le,x))),xs))))> 
     --> <Marked_a(a(not,f),b) , Marked_a(f,b)>
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(append,
                                            a(qs,a(a(filter,a(le,x)),xs))),
                                   a(a(cons,x),
                                    a(qs,a(a(filter,a(not,a(le,x))),xs))))> 
     --> <Marked_a(a(a(if,true),x),xs) , Marked_a(a(cons,x),xs)>
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(append,
                                            a(qs,a(a(filter,a(le,x)),xs))),
                                   a(a(cons,x),
                                    a(qs,a(a(filter,a(not,a(le,x))),xs))))> 
     --> <Marked_a(a(le,a(s,x)),a(s,y)) , Marked_a(a(le,x),y)>
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(append,
                                            a(qs,a(a(filter,a(le,x)),xs))),
                                   a(a(cons,x),
                                    a(qs,a(a(filter,a(not,a(le,x))),xs))))> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(filter,f),xs)>
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(append,
                                            a(qs,a(a(filter,a(le,x)),xs))),
                                   a(a(cons,x),
                                    a(qs,a(a(filter,a(not,a(le,x))),xs))))> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(f,x)>
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(append,
                                            a(qs,a(a(filter,a(le,x)),xs))),
                                   a(a(cons,x),
                                    a(qs,a(a(filter,a(not,a(le,x))),xs))))> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(if,a(f,x)),x)>
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(append,
                                            a(qs,a(a(filter,a(le,x)),xs))),
                                   a(a(cons,x),
                                    a(qs,a(a(filter,a(not,a(le,x))),xs))))> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(a(if,a(f,x)),x),
                                                   a(a(filter,f),xs))>
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(append,
                                            a(qs,a(a(filter,a(le,x)),xs))),
                                   a(a(cons,x),
                                    a(qs,a(a(filter,a(not,a(le,x))),xs))))> 
     --> <Marked_a(a(append,a(a(cons,x),xs)),ys) , Marked_a(a(append,xs),ys)>
  <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(append,
                                            a(qs,a(a(filter,a(le,x)),xs))),
                                   a(a(cons,x),
                                    a(qs,a(a(filter,a(not,a(le,x))),xs))))> 
     --> <Marked_a(a(append,a(a(cons,x),xs)),ys) , Marked_a(a(cons,x),
                                                    a(a(append,xs),ys))>
  <Marked_a(a(not,f),b) , Marked_a(f,b)> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(filter,a(not,a(le,x))),xs)>
  <Marked_a(a(not,f),b) , Marked_a(f,b)> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(qs,
                                          a(a(filter,a(not,a(le,x))),xs))>
  <Marked_a(a(not,f),b) , Marked_a(f,b)> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(cons,x),
                                          a(qs,a(a(filter,a(not,a(le,x))),xs)))>
  <Marked_a(a(not,f),b) , Marked_a(f,b)> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(filter,a(le,x)),xs)>
  <Marked_a(a(not,f),b) , Marked_a(f,b)> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(qs,a(a(filter,a(le,x)),xs))>
  <Marked_a(a(not,f),b) , Marked_a(f,b)> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(append,
                                                   a(qs,
                                                    a(a(filter,a(le,x)),xs))),
                                          a(a(cons,x),
                                           a(qs,a(a(filter,a(not,a(le,x))),xs))))
                                          >
  <Marked_a(a(not,f),b) , Marked_a(f,b)> 
     --> <Marked_a(a(not,f),b) , Marked_a(f,b)>
  <Marked_a(a(not,f),b) , Marked_a(f,b)> 
     --> <Marked_a(a(a(if,true),x),xs) , Marked_a(a(cons,x),xs)>
  <Marked_a(a(not,f),b) , Marked_a(f,b)> 
     --> <Marked_a(a(le,a(s,x)),a(s,y)) , Marked_a(a(le,x),y)>
  <Marked_a(a(not,f),b) , Marked_a(f,b)> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(filter,f),xs)>
  <Marked_a(a(not,f),b) , Marked_a(f,b)> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(f,x)>
  <Marked_a(a(not,f),b) , Marked_a(f,b)> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(if,a(f,x)),x)>
  <Marked_a(a(not,f),b) , Marked_a(f,b)> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(a(if,a(f,x)),x),
                                                   a(a(filter,f),xs))>
  <Marked_a(a(not,f),b) , Marked_a(f,b)> 
     --> <Marked_a(a(append,a(a(cons,x),xs)),ys) , Marked_a(a(append,xs),ys)>
  <Marked_a(a(not,f),b) , Marked_a(f,b)> 
     --> <Marked_a(a(append,a(a(cons,x),xs)),ys) , Marked_a(a(cons,x),
                                                    a(a(append,xs),ys))>
  <Marked_a(a(a(if,true),x),xs) , Marked_a(a(cons,x),xs)> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(filter,a(not,a(le,x))),xs)>
  <Marked_a(a(a(if,true),x),xs) , Marked_a(a(cons,x),xs)> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(qs,
                                          a(a(filter,a(not,a(le,x))),xs))>
  <Marked_a(a(a(if,true),x),xs) , Marked_a(a(cons,x),xs)> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(cons,x),
                                          a(qs,a(a(filter,a(not,a(le,x))),xs)))>
  <Marked_a(a(a(if,true),x),xs) , Marked_a(a(cons,x),xs)> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(filter,a(le,x)),xs)>
  <Marked_a(a(a(if,true),x),xs) , Marked_a(a(cons,x),xs)> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(qs,a(a(filter,a(le,x)),xs))>
  <Marked_a(a(a(if,true),x),xs) , Marked_a(a(cons,x),xs)> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(append,
                                                   a(qs,
                                                    a(a(filter,a(le,x)),xs))),
                                          a(a(cons,x),
                                           a(qs,a(a(filter,a(not,a(le,x))),xs))))
                                          >
  <Marked_a(a(a(if,true),x),xs) , Marked_a(a(cons,x),xs)> 
     --> <Marked_a(a(not,f),b) , Marked_a(f,b)>
  <Marked_a(a(a(if,true),x),xs) , Marked_a(a(cons,x),xs)> 
     --> <Marked_a(a(a(if,true),x),xs) , Marked_a(a(cons,x),xs)>
  <Marked_a(a(a(if,true),x),xs) , Marked_a(a(cons,x),xs)> 
     --> <Marked_a(a(le,a(s,x)),a(s,y)) , Marked_a(a(le,x),y)>
  <Marked_a(a(a(if,true),x),xs) , Marked_a(a(cons,x),xs)> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(filter,f),xs)>
  <Marked_a(a(a(if,true),x),xs) , Marked_a(a(cons,x),xs)> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(f,x)>
  <Marked_a(a(a(if,true),x),xs) , Marked_a(a(cons,x),xs)> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(if,a(f,x)),x)>
  <Marked_a(a(a(if,true),x),xs) , Marked_a(a(cons,x),xs)> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(a(if,a(f,x)),x),
                                                   a(a(filter,f),xs))>
  <Marked_a(a(a(if,true),x),xs) , Marked_a(a(cons,x),xs)> 
     --> <Marked_a(a(append,a(a(cons,x),xs)),ys) , Marked_a(a(append,xs),ys)>
  <Marked_a(a(a(if,true),x),xs) , Marked_a(a(cons,x),xs)> 
     --> <Marked_a(a(append,a(a(cons,x),xs)),ys) , Marked_a(a(cons,x),
                                                    a(a(append,xs),ys))>
  <Marked_a(a(le,a(s,x)),a(s,y)) , Marked_a(a(le,x),y)> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(filter,a(not,a(le,x))),xs)>
  <Marked_a(a(le,a(s,x)),a(s,y)) , Marked_a(a(le,x),y)> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(qs,
                                          a(a(filter,a(not,a(le,x))),xs))>
  <Marked_a(a(le,a(s,x)),a(s,y)) , Marked_a(a(le,x),y)> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(cons,x),
                                          a(qs,a(a(filter,a(not,a(le,x))),xs)))>
  <Marked_a(a(le,a(s,x)),a(s,y)) , Marked_a(a(le,x),y)> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(filter,a(le,x)),xs)>
  <Marked_a(a(le,a(s,x)),a(s,y)) , Marked_a(a(le,x),y)> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(qs,a(a(filter,a(le,x)),xs))>
  <Marked_a(a(le,a(s,x)),a(s,y)) , Marked_a(a(le,x),y)> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(append,
                                                   a(qs,
                                                    a(a(filter,a(le,x)),xs))),
                                          a(a(cons,x),
                                           a(qs,a(a(filter,a(not,a(le,x))),xs))))
                                          >
  <Marked_a(a(le,a(s,x)),a(s,y)) , Marked_a(a(le,x),y)> 
     --> <Marked_a(a(not,f),b) , Marked_a(f,b)>
  <Marked_a(a(le,a(s,x)),a(s,y)) , Marked_a(a(le,x),y)> 
     --> <Marked_a(a(a(if,true),x),xs) , Marked_a(a(cons,x),xs)>
  <Marked_a(a(le,a(s,x)),a(s,y)) , Marked_a(a(le,x),y)> 
     --> <Marked_a(a(le,a(s,x)),a(s,y)) , Marked_a(a(le,x),y)>
  <Marked_a(a(le,a(s,x)),a(s,y)) , Marked_a(a(le,x),y)> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(filter,f),xs)>
  <Marked_a(a(le,a(s,x)),a(s,y)) , Marked_a(a(le,x),y)> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(f,x)>
  <Marked_a(a(le,a(s,x)),a(s,y)) , Marked_a(a(le,x),y)> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(if,a(f,x)),x)>
  <Marked_a(a(le,a(s,x)),a(s,y)) , Marked_a(a(le,x),y)> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(a(if,a(f,x)),x),
                                                   a(a(filter,f),xs))>
  <Marked_a(a(le,a(s,x)),a(s,y)) , Marked_a(a(le,x),y)> 
     --> <Marked_a(a(append,a(a(cons,x),xs)),ys) , Marked_a(a(append,xs),ys)>
  <Marked_a(a(le,a(s,x)),a(s,y)) , Marked_a(a(le,x),y)> 
     --> <Marked_a(a(append,a(a(cons,x),xs)),ys) , Marked_a(a(cons,x),
                                                    a(a(append,xs),ys))>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(filter,f),xs)> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(filter,a(not,a(le,x))),xs)>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(filter,f),xs)> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(qs,
                                          a(a(filter,a(not,a(le,x))),xs))>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(filter,f),xs)> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(cons,x),
                                          a(qs,a(a(filter,a(not,a(le,x))),xs)))>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(filter,f),xs)> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(filter,a(le,x)),xs)>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(filter,f),xs)> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(qs,a(a(filter,a(le,x)),xs))>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(filter,f),xs)> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(append,
                                                   a(qs,
                                                    a(a(filter,a(le,x)),xs))),
                                          a(a(cons,x),
                                           a(qs,a(a(filter,a(not,a(le,x))),xs))))
                                          >
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(filter,f),xs)> 
     --> <Marked_a(a(not,f),b) , Marked_a(f,b)>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(filter,f),xs)> 
     --> <Marked_a(a(a(if,true),x),xs) , Marked_a(a(cons,x),xs)>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(filter,f),xs)> 
     --> <Marked_a(a(le,a(s,x)),a(s,y)) , Marked_a(a(le,x),y)>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(filter,f),xs)> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(filter,f),xs)>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(filter,f),xs)> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(f,x)>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(filter,f),xs)> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(if,a(f,x)),x)>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(filter,f),xs)> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(a(if,a(f,x)),x),
                                                   a(a(filter,f),xs))>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(filter,f),xs)> 
     --> <Marked_a(a(append,a(a(cons,x),xs)),ys) , Marked_a(a(append,xs),ys)>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(filter,f),xs)> 
     --> <Marked_a(a(append,a(a(cons,x),xs)),ys) , Marked_a(a(cons,x),
                                                    a(a(append,xs),ys))>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(f,x)> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(filter,a(not,a(le,x))),xs)>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(f,x)> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(qs,
                                          a(a(filter,a(not,a(le,x))),xs))>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(f,x)> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(cons,x),
                                          a(qs,a(a(filter,a(not,a(le,x))),xs)))>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(f,x)> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(filter,a(le,x)),xs)>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(f,x)> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(qs,a(a(filter,a(le,x)),xs))>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(f,x)> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(append,
                                                   a(qs,
                                                    a(a(filter,a(le,x)),xs))),
                                          a(a(cons,x),
                                           a(qs,a(a(filter,a(not,a(le,x))),xs))))
                                          >
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(f,x)> 
     --> <Marked_a(a(not,f),b) , Marked_a(f,b)>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(f,x)> 
     --> <Marked_a(a(a(if,true),x),xs) , Marked_a(a(cons,x),xs)>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(f,x)> 
     --> <Marked_a(a(le,a(s,x)),a(s,y)) , Marked_a(a(le,x),y)>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(f,x)> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(filter,f),xs)>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(f,x)> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(f,x)>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(f,x)> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(if,a(f,x)),x)>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(f,x)> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(a(if,a(f,x)),x),
                                                   a(a(filter,f),xs))>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(f,x)> 
     --> <Marked_a(a(append,a(a(cons,x),xs)),ys) , Marked_a(a(append,xs),ys)>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(f,x)> 
     --> <Marked_a(a(append,a(a(cons,x),xs)),ys) , Marked_a(a(cons,x),
                                                    a(a(append,xs),ys))>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(if,a(f,x)),x)> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(filter,a(not,a(le,x))),xs)>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(if,a(f,x)),x)> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(qs,
                                          a(a(filter,a(not,a(le,x))),xs))>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(if,a(f,x)),x)> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(cons,x),
                                          a(qs,a(a(filter,a(not,a(le,x))),xs)))>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(if,a(f,x)),x)> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(filter,a(le,x)),xs)>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(if,a(f,x)),x)> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(qs,a(a(filter,a(le,x)),xs))>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(if,a(f,x)),x)> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(append,
                                                   a(qs,
                                                    a(a(filter,a(le,x)),xs))),
                                          a(a(cons,x),
                                           a(qs,a(a(filter,a(not,a(le,x))),xs))))
                                          >
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(if,a(f,x)),x)> 
     --> <Marked_a(a(not,f),b) , Marked_a(f,b)>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(if,a(f,x)),x)> 
     --> <Marked_a(a(a(if,true),x),xs) , Marked_a(a(cons,x),xs)>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(if,a(f,x)),x)> 
     --> <Marked_a(a(le,a(s,x)),a(s,y)) , Marked_a(a(le,x),y)>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(if,a(f,x)),x)> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(filter,f),xs)>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(if,a(f,x)),x)> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(f,x)>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(if,a(f,x)),x)> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(if,a(f,x)),x)>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(if,a(f,x)),x)> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(a(if,a(f,x)),x),
                                                   a(a(filter,f),xs))>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(if,a(f,x)),x)> 
     --> <Marked_a(a(append,a(a(cons,x),xs)),ys) , Marked_a(a(append,xs),ys)>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(if,a(f,x)),x)> 
     --> <Marked_a(a(append,a(a(cons,x),xs)),ys) , Marked_a(a(cons,x),
                                                    a(a(append,xs),ys))>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(a(if,a(f,x)),x),
                                            a(a(filter,f),xs))> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(filter,a(not,a(le,x))),xs)>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(a(if,a(f,x)),x),
                                            a(a(filter,f),xs))> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(qs,
                                          a(a(filter,a(not,a(le,x))),xs))>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(a(if,a(f,x)),x),
                                            a(a(filter,f),xs))> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(cons,x),
                                          a(qs,a(a(filter,a(not,a(le,x))),xs)))>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(a(if,a(f,x)),x),
                                            a(a(filter,f),xs))> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(filter,a(le,x)),xs)>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(a(if,a(f,x)),x),
                                            a(a(filter,f),xs))> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(qs,a(a(filter,a(le,x)),xs))>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(a(if,a(f,x)),x),
                                            a(a(filter,f),xs))> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(append,
                                                   a(qs,
                                                    a(a(filter,a(le,x)),xs))),
                                          a(a(cons,x),
                                           a(qs,a(a(filter,a(not,a(le,x))),xs))))
                                          >
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(a(if,a(f,x)),x),
                                            a(a(filter,f),xs))> 
     --> <Marked_a(a(not,f),b) , Marked_a(f,b)>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(a(if,a(f,x)),x),
                                            a(a(filter,f),xs))> 
     --> <Marked_a(a(a(if,true),x),xs) , Marked_a(a(cons,x),xs)>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(a(if,a(f,x)),x),
                                            a(a(filter,f),xs))> 
     --> <Marked_a(a(le,a(s,x)),a(s,y)) , Marked_a(a(le,x),y)>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(a(if,a(f,x)),x),
                                            a(a(filter,f),xs))> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(filter,f),xs)>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(a(if,a(f,x)),x),
                                            a(a(filter,f),xs))> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(f,x)>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(a(if,a(f,x)),x),
                                            a(a(filter,f),xs))> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(if,a(f,x)),x)>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(a(if,a(f,x)),x),
                                            a(a(filter,f),xs))> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(a(if,a(f,x)),x),
                                                   a(a(filter,f),xs))>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(a(if,a(f,x)),x),
                                            a(a(filter,f),xs))> 
     --> <Marked_a(a(append,a(a(cons,x),xs)),ys) , Marked_a(a(append,xs),ys)>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(a(if,a(f,x)),x),
                                            a(a(filter,f),xs))> 
     --> <Marked_a(a(append,a(a(cons,x),xs)),ys) , Marked_a(a(cons,x),
                                                    a(a(append,xs),ys))>
  <Marked_a(a(append,a(a(cons,x),xs)),ys) , Marked_a(a(append,xs),ys)> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(filter,a(not,a(le,x))),xs)>
  <Marked_a(a(append,a(a(cons,x),xs)),ys) , Marked_a(a(append,xs),ys)> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(qs,
                                          a(a(filter,a(not,a(le,x))),xs))>
  <Marked_a(a(append,a(a(cons,x),xs)),ys) , Marked_a(a(append,xs),ys)> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(cons,x),
                                          a(qs,a(a(filter,a(not,a(le,x))),xs)))>
  <Marked_a(a(append,a(a(cons,x),xs)),ys) , Marked_a(a(append,xs),ys)> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(filter,a(le,x)),xs)>
  <Marked_a(a(append,a(a(cons,x),xs)),ys) , Marked_a(a(append,xs),ys)> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(qs,a(a(filter,a(le,x)),xs))>
  <Marked_a(a(append,a(a(cons,x),xs)),ys) , Marked_a(a(append,xs),ys)> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(append,
                                                   a(qs,
                                                    a(a(filter,a(le,x)),xs))),
                                          a(a(cons,x),
                                           a(qs,a(a(filter,a(not,a(le,x))),xs))))
                                          >
  <Marked_a(a(append,a(a(cons,x),xs)),ys) , Marked_a(a(append,xs),ys)> 
     --> <Marked_a(a(not,f),b) , Marked_a(f,b)>
  <Marked_a(a(append,a(a(cons,x),xs)),ys) , Marked_a(a(append,xs),ys)> 
     --> <Marked_a(a(a(if,true),x),xs) , Marked_a(a(cons,x),xs)>
  <Marked_a(a(append,a(a(cons,x),xs)),ys) , Marked_a(a(append,xs),ys)> 
     --> <Marked_a(a(le,a(s,x)),a(s,y)) , Marked_a(a(le,x),y)>
  <Marked_a(a(append,a(a(cons,x),xs)),ys) , Marked_a(a(append,xs),ys)> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(filter,f),xs)>
  <Marked_a(a(append,a(a(cons,x),xs)),ys) , Marked_a(a(append,xs),ys)> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(f,x)>
  <Marked_a(a(append,a(a(cons,x),xs)),ys) , Marked_a(a(append,xs),ys)> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(if,a(f,x)),x)>
  <Marked_a(a(append,a(a(cons,x),xs)),ys) , Marked_a(a(append,xs),ys)> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(a(if,a(f,x)),x),
                                                   a(a(filter,f),xs))>
  <Marked_a(a(append,a(a(cons,x),xs)),ys) , Marked_a(a(append,xs),ys)> 
     --> <Marked_a(a(append,a(a(cons,x),xs)),ys) , Marked_a(a(append,xs),ys)>
  <Marked_a(a(append,a(a(cons,x),xs)),ys) , Marked_a(a(append,xs),ys)> 
     --> <Marked_a(a(append,a(a(cons,x),xs)),ys) , Marked_a(a(cons,x),
                                                    a(a(append,xs),ys))>
  <Marked_a(a(append,a(a(cons,x),xs)),ys) , Marked_a(a(cons,x),
                                             a(a(append,xs),ys))> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(filter,a(not,a(le,x))),xs)>
  <Marked_a(a(append,a(a(cons,x),xs)),ys) , Marked_a(a(cons,x),
                                             a(a(append,xs),ys))> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(qs,
                                          a(a(filter,a(not,a(le,x))),xs))>
  <Marked_a(a(append,a(a(cons,x),xs)),ys) , Marked_a(a(cons,x),
                                             a(a(append,xs),ys))> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(cons,x),
                                          a(qs,a(a(filter,a(not,a(le,x))),xs)))>
  <Marked_a(a(append,a(a(cons,x),xs)),ys) , Marked_a(a(cons,x),
                                             a(a(append,xs),ys))> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(filter,a(le,x)),xs)>
  <Marked_a(a(append,a(a(cons,x),xs)),ys) , Marked_a(a(cons,x),
                                             a(a(append,xs),ys))> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(qs,a(a(filter,a(le,x)),xs))>
  <Marked_a(a(append,a(a(cons,x),xs)),ys) , Marked_a(a(cons,x),
                                             a(a(append,xs),ys))> 
     --> <Marked_a(qs,a(a(cons,x),xs)) , Marked_a(a(append,
                                                   a(qs,
                                                    a(a(filter,a(le,x)),xs))),
                                          a(a(cons,x),
                                           a(qs,a(a(filter,a(not,a(le,x))),xs))))
                                          >
  <Marked_a(a(append,a(a(cons,x),xs)),ys) , Marked_a(a(cons,x),
                                             a(a(append,xs),ys))> 
     --> <Marked_a(a(not,f),b) , Marked_a(f,b)>
  <Marked_a(a(append,a(a(cons,x),xs)),ys) , Marked_a(a(cons,x),
                                             a(a(append,xs),ys))> 
     --> <Marked_a(a(a(if,true),x),xs) , Marked_a(a(cons,x),xs)>
  <Marked_a(a(append,a(a(cons,x),xs)),ys) , Marked_a(a(cons,x),
                                             a(a(append,xs),ys))> 
     --> <Marked_a(a(le,a(s,x)),a(s,y)) , Marked_a(a(le,x),y)>
  <Marked_a(a(append,a(a(cons,x),xs)),ys) , Marked_a(a(cons,x),
                                             a(a(append,xs),ys))> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(filter,f),xs)>
  <Marked_a(a(append,a(a(cons,x),xs)),ys) , Marked_a(a(cons,x),
                                             a(a(append,xs),ys))> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(f,x)>
  <Marked_a(a(append,a(a(cons,x),xs)),ys) , Marked_a(a(cons,x),
                                             a(a(append,xs),ys))> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(if,a(f,x)),x)>
  <Marked_a(a(append,a(a(cons,x),xs)),ys) , Marked_a(a(cons,x),
                                             a(a(append,xs),ys))> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(a(if,a(f,x)),x),
                                                   a(a(filter,f),xs))>
  <Marked_a(a(append,a(a(cons,x),xs)),ys) , Marked_a(a(cons,x),
                                             a(a(append,xs),ys))> 
     --> <Marked_a(a(append,a(a(cons,x),xs)),ys) , Marked_a(a(append,xs),ys)>
  <Marked_a(a(append,a(a(cons,x),xs)),ys) , Marked_a(a(cons,x),
                                             a(a(append,xs),ys))> 
     --> <Marked_a(a(append,a(a(cons,x),xs)),ys) , Marked_a(a(cons,x),
                                                    a(a(append,xs),ys))>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  a(a(a(if,true),x),xs) >= a(a(cons,x),xs) ;
  a(a(a(if,false),x),xs) >= xs ;
  a(a(append,a(a(cons,x),xs)),ys) >= a(a(cons,x),a(a(append,xs),ys)) ;
  a(a(append,nil),ys) >= ys ;
  a(a(filter,f),a(a(cons,x),xs)) >= a(a(a(if,a(f,x)),x),a(a(filter,f),xs)) ;
  a(a(filter,f),nil) >= nil ;
  a(a(le,a(s,x)),a(s,y)) >= a(a(le,x),y) ;
  a(a(le,a(s,x)),0) >= false ;
  a(a(le,0),y) >= true ;
  a(a(not,f),b) >= a(not2,a(f,b)) ;
  a(not2,true) >= false ;
  a(not2,false) >= true ;
  a(qs,a(a(cons,x),xs)) >= a(a(append,a(qs,a(a(filter,a(le,x)),xs))),
                            a(a(cons,x),a(qs,a(a(filter,a(not,a(le,x))),xs)))) ;
  a(qs,nil) >= nil ;
  Marked_a(a(a(if,true),x),xs) >= Marked_a(a(cons,x),xs) ;
  Marked_a(a(append,a(a(cons,x),xs)),ys) >= Marked_a(a(append,xs),ys) ;
  Marked_a(a(append,a(a(cons,x),xs)),ys) >= Marked_a(a(cons,x),
                                             a(a(append,xs),ys)) ;
  Marked_a(a(filter,f),a(a(cons,x),xs)) >= Marked_a(a(a(if,a(f,x)),x),
                                            a(a(filter,f),xs)) ;
  Marked_a(a(filter,f),a(a(cons,x),xs)) >= Marked_a(a(filter,f),xs) ;
  Marked_a(a(filter,f),a(a(cons,x),xs)) >= Marked_a(a(if,a(f,x)),x) ;
  Marked_a(a(filter,f),a(a(cons,x),xs)) >= Marked_a(f,x) ;
  Marked_a(a(le,a(s,x)),a(s,y)) >= Marked_a(a(le,x),y) ;
  Marked_a(a(not,f),b) >= Marked_a(f,b) ;
  Marked_a(qs,a(a(cons,x),xs)) >= Marked_a(a(append,
                                            a(qs,a(a(filter,a(le,x)),xs))),
                                   a(a(cons,x),
                                    a(qs,a(a(filter,a(not,a(le,x))),xs)))) ;
  Marked_a(qs,a(a(cons,x),xs)) >= Marked_a(a(cons,x),
                                   a(qs,a(a(filter,a(not,a(le,x))),xs))) ;
  Marked_a(qs,a(a(cons,x),xs)) >= Marked_a(a(filter,a(le,x)),xs) ;
  Marked_a(qs,a(a(cons,x),xs)) >= Marked_a(a(filter,a(not,a(le,x))),xs) ;
  Marked_a(qs,a(a(cons,x),xs)) >= Marked_a(qs,a(a(filter,a(le,x)),xs)) ;
  Marked_a(qs,a(a(cons,x),xs)) >= Marked_a(qs,a(a(filter,a(not,a(le,x))),xs)) ;
 }
 + Disjunctions:{ 
{
  Marked_a(a(a(if,true),x),xs) > Marked_a(a(cons,x),xs) ;
 }
{
  Marked_a(a(append,a(a(cons,x),xs)),ys) > Marked_a(a(append,xs),ys) ;
 }
{
  Marked_a(a(append,a(a(cons,x),xs)),ys) > Marked_a(a(cons,x),
                                            a(a(append,xs),ys)) ;
 }
{
  Marked_a(a(filter,f),a(a(cons,x),xs)) > Marked_a(a(a(if,a(f,x)),x),
                                           a(a(filter,f),xs)) ;
 }
{
  Marked_a(a(filter,f),a(a(cons,x),xs)) > Marked_a(a(filter,f),xs) ;
 }
{
  Marked_a(a(filter,f),a(a(cons,x),xs)) > Marked_a(a(if,a(f,x)),x) ;
 }
{
  Marked_a(a(filter,f),a(a(cons,x),xs)) > Marked_a(f,x) ;
 }
{
  Marked_a(a(le,a(s,x)),a(s,y)) > Marked_a(a(le,x),y) ;
 }
{
  Marked_a(a(not,f),b) > Marked_a(f,b) ;
 }
{
  Marked_a(qs,a(a(cons,x),xs)) > Marked_a(a(append,
                                           a(qs,a(a(filter,a(le,x)),xs))),
                                  a(a(cons,x),
                                   a(qs,a(a(filter,a(not,a(le,x))),xs)))) ;
 }
{
  Marked_a(qs,a(a(cons,x),xs)) > Marked_a(a(cons,x),
                                  a(qs,a(a(filter,a(not,a(le,x))),xs))) ;
 }
{
  Marked_a(qs,a(a(cons,x),xs)) > Marked_a(a(filter,a(le,x)),xs) ;
 }
{
  Marked_a(qs,a(a(cons,x),xs)) > Marked_a(a(filter,a(not,a(le,x))),xs) ;
 }
{
  Marked_a(qs,a(a(cons,x),xs)) > Marked_a(qs,a(a(filter,a(le,x)),xs)) ;
 }
{
  Marked_a(qs,a(a(cons,x),xs)) > Marked_a(qs,a(a(filter,a(not,a(le,x))),xs)) ;
 }
 } 
=== 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 : 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
=== 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
=== 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 65.863296 seconds (real time)
Cime Exit Status: 0