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

TRS termination of:
[1] a(a(divides,0),a(s,y)) -> true
[2] a(a(divides,a(s,x)),a(s,y)) -> a(a(a(div2,x),a(s,y)),y)
[3] a(a(a(div2,x),y),0) -> a(a(divides,x),y)
[4] a(a(a(div2,0),y),a(s,z)) -> false
[5] a(a(a(div2,a(s,x)),y),a(s,z)) -> a(a(a(div2,x),y),z)
[6] a(a(filter,f),nil) -> nil
[7] a(a(filter,f),a(a(cons,x),xs)) -> a(a(a(if,a(f,x)),x),a(a(filter,f),xs))
[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),x) -> a(not2,a(f,x))
[11] a(not2,true) -> false
[12] a(not2,false) -> true
[13] a(sieve,nil) -> nil
[14] a(sieve,a(a(cons,x),xs)) ->
 a(a(cons,x),a(sieve,a(a(filter,a(not,a(divides,x))),xs)))


Sub problem: 
guided: 

DP termination of:
<Marked_a(a(divides,a(s,x)),a(s,y)) , Marked_a(a(a(div2,x),a(s,y)),y)>
<Marked_a(a(divides,a(s,x)),a(s,y)) , Marked_a(a(div2,x),a(s,y))>
<Marked_a(a(divides,a(s,x)),a(s,y)) , Marked_a(div2,x)>
<Marked_a(a(a(div2,x),y),0) , Marked_a(a(divides,x),y)>
<Marked_a(a(a(div2,x),y),0) , Marked_a(divides,x)>
<Marked_a(a(a(div2,a(s,x)),y),a(s,z)) , Marked_a(a(a(div2,x),y),z)>
<Marked_a(a(a(div2,a(s,x)),y),a(s,z)) , Marked_a(a(div2,x),y)>
<Marked_a(a(a(div2,a(s,x)),y),a(s,z)) , Marked_a(div2,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(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(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),x) , Marked_a(not2,a(f,x))>
<Marked_a(a(not,f),x) , Marked_a(f,x)>
<Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(a(cons,x),
                                    a(sieve,
                                     a(a(filter,a(not,a(divides,x))),xs)))>
<Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(sieve,
                                    a(a(filter,a(not,a(divides,x))),xs))>
<Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(a(filter,a(not,a(divides,x))),xs)>
<Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(filter,a(not,a(divides,x)))>
<Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(not,a(divides,x))>
<Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(divides,x)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(a(filter,a(not,a(divides,x))),
                                       xs)> 
      --> <Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(a(filter,
                                                       a(not,a(divides,x))),
                                              xs)>
  <Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(a(filter,a(not,a(divides,x))),xs)> 
     --> <Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(sieve,
                                             a(a(filter,a(not,a(divides,x))),
                                              xs))>
  <Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(a(filter,a(not,a(divides,x))),xs)> 
     --> <Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(a(cons,x),
                                             a(sieve,
                                              a(a(filter,a(not,a(divides,x))),
                                               xs)))>
  <Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(a(filter,a(not,a(divides,x))),xs)> 
     --> <Marked_a(a(not,f),x) , Marked_a(f,x)>
  <Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(a(filter,a(not,a(divides,x))),xs)> 
     --> <Marked_a(a(a(if,true),x),xs) , Marked_a(a(cons,x),xs)>
  <Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(a(filter,a(not,a(divides,x))),xs)> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(filter,f),xs)>
  <Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(a(filter,a(not,a(divides,x))),xs)> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(f,x)>
  <Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(a(filter,a(not,a(divides,x))),xs)> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(if,a(f,x)),x)>
  <Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(a(filter,a(not,a(divides,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(sieve,a(a(cons,x),xs)) , Marked_a(a(filter,a(not,a(divides,x))),xs)> 
     --> <Marked_a(a(a(div2,a(s,x)),y),a(s,z)) , Marked_a(a(div2,x),y)>
  <Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(a(filter,a(not,a(divides,x))),xs)> 
     --> <Marked_a(a(a(div2,a(s,x)),y),a(s,z)) , Marked_a(a(a(div2,x),y),z)>
  <Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(a(filter,a(not,a(divides,x))),xs)> 
     --> <Marked_a(a(a(div2,x),y),0) , Marked_a(a(divides,x),y)>
  <Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(a(filter,a(not,a(divides,x))),xs)> 
     --> <Marked_a(a(divides,a(s,x)),a(s,y)) , Marked_a(a(div2,x),a(s,y))>
  <Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(a(filter,a(not,a(divides,x))),xs)> 
     --> <Marked_a(a(divides,a(s,x)),a(s,y)) , Marked_a(a(a(div2,x),a(s,y)),y)>
  <Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(sieve,
                                      a(a(filter,a(not,a(divides,x))),xs))> 
     --> <Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(a(filter,
                                                      a(not,a(divides,x))),
                                             xs)>
  <Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(sieve,
                                      a(a(filter,a(not,a(divides,x))),xs))> 
     --> <Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(sieve,
                                             a(a(filter,a(not,a(divides,x))),
                                              xs))>
  <Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(sieve,
                                      a(a(filter,a(not,a(divides,x))),xs))> 
     --> <Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(a(cons,x),
                                             a(sieve,
                                              a(a(filter,a(not,a(divides,x))),
                                               xs)))>
  <Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(a(cons,x),
                                      a(sieve,
                                       a(a(filter,a(not,a(divides,x))),xs)))> 
     --> <Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(a(filter,
                                                      a(not,a(divides,x))),
                                             xs)>
  <Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(a(cons,x),
                                      a(sieve,
                                       a(a(filter,a(not,a(divides,x))),xs)))> 
     --> <Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(sieve,
                                             a(a(filter,a(not,a(divides,x))),
                                              xs))>
  <Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(a(cons,x),
                                      a(sieve,
                                       a(a(filter,a(not,a(divides,x))),xs)))> 
     --> <Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(a(cons,x),
                                             a(sieve,
                                              a(a(filter,a(not,a(divides,x))),
                                               xs)))>
  <Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(a(cons,x),
                                      a(sieve,
                                       a(a(filter,a(not,a(divides,x))),xs)))> 
     --> <Marked_a(a(not,f),x) , Marked_a(f,x)>
  <Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(a(cons,x),
                                      a(sieve,
                                       a(a(filter,a(not,a(divides,x))),xs)))> 
     --> <Marked_a(a(a(if,true),x),xs) , Marked_a(a(cons,x),xs)>
  <Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(a(cons,x),
                                      a(sieve,
                                       a(a(filter,a(not,a(divides,x))),xs)))> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(filter,f),xs)>
  <Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(a(cons,x),
                                      a(sieve,
                                       a(a(filter,a(not,a(divides,x))),xs)))> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(f,x)>
  <Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(a(cons,x),
                                      a(sieve,
                                       a(a(filter,a(not,a(divides,x))),xs)))> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(if,a(f,x)),x)>
  <Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(a(cons,x),
                                      a(sieve,
                                       a(a(filter,a(not,a(divides,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(sieve,a(a(cons,x),xs)) , Marked_a(a(cons,x),
                                      a(sieve,
                                       a(a(filter,a(not,a(divides,x))),xs)))> 
     --> <Marked_a(a(a(div2,a(s,x)),y),a(s,z)) , Marked_a(a(div2,x),y)>
  <Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(a(cons,x),
                                      a(sieve,
                                       a(a(filter,a(not,a(divides,x))),xs)))> 
     --> <Marked_a(a(a(div2,a(s,x)),y),a(s,z)) , Marked_a(a(a(div2,x),y),z)>
  <Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(a(cons,x),
                                      a(sieve,
                                       a(a(filter,a(not,a(divides,x))),xs)))> 
     --> <Marked_a(a(a(div2,x),y),0) , Marked_a(a(divides,x),y)>
  <Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(a(cons,x),
                                      a(sieve,
                                       a(a(filter,a(not,a(divides,x))),xs)))> 
     --> <Marked_a(a(divides,a(s,x)),a(s,y)) , Marked_a(a(div2,x),a(s,y))>
  <Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(a(cons,x),
                                      a(sieve,
                                       a(a(filter,a(not,a(divides,x))),xs)))> 
     --> <Marked_a(a(divides,a(s,x)),a(s,y)) , Marked_a(a(a(div2,x),a(s,y)),y)>
  <Marked_a(a(not,f),x) , Marked_a(f,x)> 
     --> <Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(a(filter,
                                                      a(not,a(divides,x))),
                                             xs)>
  <Marked_a(a(not,f),x) , Marked_a(f,x)> 
     --> <Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(sieve,
                                             a(a(filter,a(not,a(divides,x))),
                                              xs))>
  <Marked_a(a(not,f),x) , Marked_a(f,x)> 
     --> <Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(a(cons,x),
                                             a(sieve,
                                              a(a(filter,a(not,a(divides,x))),
                                               xs)))>
  <Marked_a(a(not,f),x) , Marked_a(f,x)> 
     --> <Marked_a(a(not,f),x) , Marked_a(f,x)>
  <Marked_a(a(not,f),x) , Marked_a(f,x)> 
     --> <Marked_a(a(a(if,true),x),xs) , Marked_a(a(cons,x),xs)>
  <Marked_a(a(not,f),x) , Marked_a(f,x)> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(filter,f),xs)>
  <Marked_a(a(not,f),x) , Marked_a(f,x)> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(f,x)>
  <Marked_a(a(not,f),x) , 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(not,f),x) , 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(not,f),x) , Marked_a(f,x)> 
     --> <Marked_a(a(a(div2,a(s,x)),y),a(s,z)) , Marked_a(a(div2,x),y)>
  <Marked_a(a(not,f),x) , Marked_a(f,x)> 
     --> <Marked_a(a(a(div2,a(s,x)),y),a(s,z)) , Marked_a(a(a(div2,x),y),z)>
  <Marked_a(a(not,f),x) , Marked_a(f,x)> 
     --> <Marked_a(a(a(div2,x),y),0) , Marked_a(a(divides,x),y)>
  <Marked_a(a(not,f),x) , Marked_a(f,x)> 
     --> <Marked_a(a(divides,a(s,x)),a(s,y)) , Marked_a(a(div2,x),a(s,y))>
  <Marked_a(a(not,f),x) , Marked_a(f,x)> 
     --> <Marked_a(a(divides,a(s,x)),a(s,y)) , Marked_a(a(a(div2,x),a(s,y)),y)>
  <Marked_a(a(a(if,true),x),xs) , Marked_a(a(cons,x),xs)> 
     --> <Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(a(filter,
                                                      a(not,a(divides,x))),
                                             xs)>
  <Marked_a(a(a(if,true),x),xs) , Marked_a(a(cons,x),xs)> 
     --> <Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(sieve,
                                             a(a(filter,a(not,a(divides,x))),
                                              xs))>
  <Marked_a(a(a(if,true),x),xs) , Marked_a(a(cons,x),xs)> 
     --> <Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(a(cons,x),
                                             a(sieve,
                                              a(a(filter,a(not,a(divides,x))),
                                               xs)))>
  <Marked_a(a(a(if,true),x),xs) , Marked_a(a(cons,x),xs)> 
     --> <Marked_a(a(not,f),x) , Marked_a(f,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(a(cons,x),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(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(a(div2,a(s,x)),y),a(s,z)) , Marked_a(a(div2,x),y)>
  <Marked_a(a(a(if,true),x),xs) , Marked_a(a(cons,x),xs)> 
     --> <Marked_a(a(a(div2,a(s,x)),y),a(s,z)) , Marked_a(a(a(div2,x),y),z)>
  <Marked_a(a(a(if,true),x),xs) , Marked_a(a(cons,x),xs)> 
     --> <Marked_a(a(a(div2,x),y),0) , Marked_a(a(divides,x),y)>
  <Marked_a(a(a(if,true),x),xs) , Marked_a(a(cons,x),xs)> 
     --> <Marked_a(a(divides,a(s,x)),a(s,y)) , Marked_a(a(div2,x),a(s,y))>
  <Marked_a(a(a(if,true),x),xs) , Marked_a(a(cons,x),xs)> 
     --> <Marked_a(a(divides,a(s,x)),a(s,y)) , Marked_a(a(a(div2,x),a(s,y)),y)>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(filter,f),xs)> 
     --> <Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(a(filter,
                                                      a(not,a(divides,x))),
                                             xs)>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(filter,f),xs)> 
     --> <Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(sieve,
                                             a(a(filter,a(not,a(divides,x))),
                                              xs))>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(filter,f),xs)> 
     --> <Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(a(cons,x),
                                             a(sieve,
                                              a(a(filter,a(not,a(divides,x))),
                                               xs)))>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(filter,f),xs)> 
     --> <Marked_a(a(not,f),x) , Marked_a(f,x)>
  <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(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(a(div2,a(s,x)),y),a(s,z)) , Marked_a(a(div2,x),y)>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(filter,f),xs)> 
     --> <Marked_a(a(a(div2,a(s,x)),y),a(s,z)) , Marked_a(a(a(div2,x),y),z)>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(filter,f),xs)> 
     --> <Marked_a(a(a(div2,x),y),0) , Marked_a(a(divides,x),y)>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(filter,f),xs)> 
     --> <Marked_a(a(divides,a(s,x)),a(s,y)) , Marked_a(a(div2,x),a(s,y))>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(filter,f),xs)> 
     --> <Marked_a(a(divides,a(s,x)),a(s,y)) , Marked_a(a(a(div2,x),a(s,y)),y)>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(f,x)> 
     --> <Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(a(filter,
                                                      a(not,a(divides,x))),
                                             xs)>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(f,x)> 
     --> <Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(sieve,
                                             a(a(filter,a(not,a(divides,x))),
                                              xs))>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(f,x)> 
     --> <Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(a(cons,x),
                                             a(sieve,
                                              a(a(filter,a(not,a(divides,x))),
                                               xs)))>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(f,x)> 
     --> <Marked_a(a(not,f),x) , Marked_a(f,x)>
  <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(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(a(div2,a(s,x)),y),a(s,z)) , Marked_a(a(div2,x),y)>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(f,x)> 
     --> <Marked_a(a(a(div2,a(s,x)),y),a(s,z)) , Marked_a(a(a(div2,x),y),z)>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(f,x)> 
     --> <Marked_a(a(a(div2,x),y),0) , Marked_a(a(divides,x),y)>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(f,x)> 
     --> <Marked_a(a(divides,a(s,x)),a(s,y)) , Marked_a(a(div2,x),a(s,y))>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(f,x)> 
     --> <Marked_a(a(divides,a(s,x)),a(s,y)) , Marked_a(a(a(div2,x),a(s,y)),y)>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(if,a(f,x)),x)> 
     --> <Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(a(filter,
                                                      a(not,a(divides,x))),
                                             xs)>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(if,a(f,x)),x)> 
     --> <Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(sieve,
                                             a(a(filter,a(not,a(divides,x))),
                                              xs))>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(if,a(f,x)),x)> 
     --> <Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(a(cons,x),
                                             a(sieve,
                                              a(a(filter,a(not,a(divides,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),x) , 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(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(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(a(div2,a(s,x)),y),a(s,z)) , Marked_a(a(div2,x),y)>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(if,a(f,x)),x)> 
     --> <Marked_a(a(a(div2,a(s,x)),y),a(s,z)) , Marked_a(a(a(div2,x),y),z)>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(if,a(f,x)),x)> 
     --> <Marked_a(a(a(div2,x),y),0) , Marked_a(a(divides,x),y)>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(if,a(f,x)),x)> 
     --> <Marked_a(a(divides,a(s,x)),a(s,y)) , Marked_a(a(div2,x),a(s,y))>
  <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(if,a(f,x)),x)> 
     --> <Marked_a(a(divides,a(s,x)),a(s,y)) , Marked_a(a(a(div2,x),a(s,y)),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(sieve,a(a(cons,x),xs)) , Marked_a(a(filter,
                                                      a(not,a(divides,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(sieve,a(a(cons,x),xs)) , Marked_a(sieve,
                                             a(a(filter,a(not,a(divides,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(sieve,a(a(cons,x),xs)) , Marked_a(a(cons,x),
                                             a(sieve,
                                              a(a(filter,a(not,a(divides,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),x) , 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(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(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(a(div2,a(s,x)),y),a(s,z)) , Marked_a(a(div2,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(a(div2,a(s,x)),y),a(s,z)) , Marked_a(a(a(div2,x),y),z)>
  <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(div2,x),y),0) , Marked_a(a(divides,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(divides,a(s,x)),a(s,y)) , Marked_a(a(div2,x),a(s,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(divides,a(s,x)),a(s,y)) , Marked_a(a(a(div2,x),a(s,y)),y)>
  <Marked_a(a(a(div2,a(s,x)),y),a(s,z)) , Marked_a(a(div2,x),y)> 
     --> <Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(a(filter,
                                                      a(not,a(divides,x))),
                                             xs)>
  <Marked_a(a(a(div2,a(s,x)),y),a(s,z)) , Marked_a(a(div2,x),y)> 
     --> <Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(sieve,
                                             a(a(filter,a(not,a(divides,x))),
                                              xs))>
  <Marked_a(a(a(div2,a(s,x)),y),a(s,z)) , Marked_a(a(div2,x),y)> 
     --> <Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(a(cons,x),
                                             a(sieve,
                                              a(a(filter,a(not,a(divides,x))),
                                               xs)))>
  <Marked_a(a(a(div2,a(s,x)),y),a(s,z)) , Marked_a(a(div2,x),y)> 
     --> <Marked_a(a(not,f),x) , Marked_a(f,x)>
  <Marked_a(a(a(div2,a(s,x)),y),a(s,z)) , Marked_a(a(div2,x),y)> 
     --> <Marked_a(a(a(if,true),x),xs) , Marked_a(a(cons,x),xs)>
  <Marked_a(a(a(div2,a(s,x)),y),a(s,z)) , Marked_a(a(div2,x),y)> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(filter,f),xs)>
  <Marked_a(a(a(div2,a(s,x)),y),a(s,z)) , Marked_a(a(div2,x),y)> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(f,x)>
  <Marked_a(a(a(div2,a(s,x)),y),a(s,z)) , Marked_a(a(div2,x),y)> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(if,a(f,x)),x)>
  <Marked_a(a(a(div2,a(s,x)),y),a(s,z)) , Marked_a(a(div2,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(a(div2,a(s,x)),y),a(s,z)) , Marked_a(a(div2,x),y)> 
     --> <Marked_a(a(a(div2,a(s,x)),y),a(s,z)) , Marked_a(a(div2,x),y)>
  <Marked_a(a(a(div2,a(s,x)),y),a(s,z)) , Marked_a(a(div2,x),y)> 
     --> <Marked_a(a(a(div2,a(s,x)),y),a(s,z)) , Marked_a(a(a(div2,x),y),z)>
  <Marked_a(a(a(div2,a(s,x)),y),a(s,z)) , Marked_a(a(div2,x),y)> 
     --> <Marked_a(a(a(div2,x),y),0) , Marked_a(a(divides,x),y)>
  <Marked_a(a(a(div2,a(s,x)),y),a(s,z)) , Marked_a(a(div2,x),y)> 
     --> <Marked_a(a(divides,a(s,x)),a(s,y)) , Marked_a(a(div2,x),a(s,y))>
  <Marked_a(a(a(div2,a(s,x)),y),a(s,z)) , Marked_a(a(div2,x),y)> 
     --> <Marked_a(a(divides,a(s,x)),a(s,y)) , Marked_a(a(a(div2,x),a(s,y)),y)>
  <Marked_a(a(a(div2,a(s,x)),y),a(s,z)) , Marked_a(a(a(div2,x),y),z)> 
     --> <Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(a(filter,
                                                      a(not,a(divides,x))),
                                             xs)>
  <Marked_a(a(a(div2,a(s,x)),y),a(s,z)) , Marked_a(a(a(div2,x),y),z)> 
     --> <Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(sieve,
                                             a(a(filter,a(not,a(divides,x))),
                                              xs))>
  <Marked_a(a(a(div2,a(s,x)),y),a(s,z)) , Marked_a(a(a(div2,x),y),z)> 
     --> <Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(a(cons,x),
                                             a(sieve,
                                              a(a(filter,a(not,a(divides,x))),
                                               xs)))>
  <Marked_a(a(a(div2,a(s,x)),y),a(s,z)) , Marked_a(a(a(div2,x),y),z)> 
     --> <Marked_a(a(not,f),x) , Marked_a(f,x)>
  <Marked_a(a(a(div2,a(s,x)),y),a(s,z)) , Marked_a(a(a(div2,x),y),z)> 
     --> <Marked_a(a(a(if,true),x),xs) , Marked_a(a(cons,x),xs)>
  <Marked_a(a(a(div2,a(s,x)),y),a(s,z)) , Marked_a(a(a(div2,x),y),z)> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(filter,f),xs)>
  <Marked_a(a(a(div2,a(s,x)),y),a(s,z)) , Marked_a(a(a(div2,x),y),z)> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(f,x)>
  <Marked_a(a(a(div2,a(s,x)),y),a(s,z)) , Marked_a(a(a(div2,x),y),z)> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(if,a(f,x)),x)>
  <Marked_a(a(a(div2,a(s,x)),y),a(s,z)) , Marked_a(a(a(div2,x),y),z)> 
     --> <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(div2,a(s,x)),y),a(s,z)) , Marked_a(a(a(div2,x),y),z)> 
     --> <Marked_a(a(a(div2,a(s,x)),y),a(s,z)) , Marked_a(a(div2,x),y)>
  <Marked_a(a(a(div2,a(s,x)),y),a(s,z)) , Marked_a(a(a(div2,x),y),z)> 
     --> <Marked_a(a(a(div2,a(s,x)),y),a(s,z)) , Marked_a(a(a(div2,x),y),z)>
  <Marked_a(a(a(div2,a(s,x)),y),a(s,z)) , Marked_a(a(a(div2,x),y),z)> 
     --> <Marked_a(a(a(div2,x),y),0) , Marked_a(a(divides,x),y)>
  <Marked_a(a(a(div2,a(s,x)),y),a(s,z)) , Marked_a(a(a(div2,x),y),z)> 
     --> <Marked_a(a(divides,a(s,x)),a(s,y)) , Marked_a(a(div2,x),a(s,y))>
  <Marked_a(a(a(div2,a(s,x)),y),a(s,z)) , Marked_a(a(a(div2,x),y),z)> 
     --> <Marked_a(a(divides,a(s,x)),a(s,y)) , Marked_a(a(a(div2,x),a(s,y)),y)>
  <Marked_a(a(a(div2,x),y),0) , Marked_a(a(divides,x),y)> 
     --> <Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(a(filter,
                                                      a(not,a(divides,x))),
                                             xs)>
  <Marked_a(a(a(div2,x),y),0) , Marked_a(a(divides,x),y)> 
     --> <Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(sieve,
                                             a(a(filter,a(not,a(divides,x))),
                                              xs))>
  <Marked_a(a(a(div2,x),y),0) , Marked_a(a(divides,x),y)> 
     --> <Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(a(cons,x),
                                             a(sieve,
                                              a(a(filter,a(not,a(divides,x))),
                                               xs)))>
  <Marked_a(a(a(div2,x),y),0) , Marked_a(a(divides,x),y)> 
     --> <Marked_a(a(not,f),x) , Marked_a(f,x)>
  <Marked_a(a(a(div2,x),y),0) , Marked_a(a(divides,x),y)> 
     --> <Marked_a(a(a(if,true),x),xs) , Marked_a(a(cons,x),xs)>
  <Marked_a(a(a(div2,x),y),0) , Marked_a(a(divides,x),y)> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(filter,f),xs)>
  <Marked_a(a(a(div2,x),y),0) , Marked_a(a(divides,x),y)> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(f,x)>
  <Marked_a(a(a(div2,x),y),0) , Marked_a(a(divides,x),y)> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(if,a(f,x)),x)>
  <Marked_a(a(a(div2,x),y),0) , Marked_a(a(divides,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(a(div2,x),y),0) , Marked_a(a(divides,x),y)> 
     --> <Marked_a(a(a(div2,a(s,x)),y),a(s,z)) , Marked_a(a(div2,x),y)>
  <Marked_a(a(a(div2,x),y),0) , Marked_a(a(divides,x),y)> 
     --> <Marked_a(a(a(div2,a(s,x)),y),a(s,z)) , Marked_a(a(a(div2,x),y),z)>
  <Marked_a(a(a(div2,x),y),0) , Marked_a(a(divides,x),y)> 
     --> <Marked_a(a(a(div2,x),y),0) , Marked_a(a(divides,x),y)>
  <Marked_a(a(a(div2,x),y),0) , Marked_a(a(divides,x),y)> 
     --> <Marked_a(a(divides,a(s,x)),a(s,y)) , Marked_a(a(div2,x),a(s,y))>
  <Marked_a(a(a(div2,x),y),0) , Marked_a(a(divides,x),y)> 
     --> <Marked_a(a(divides,a(s,x)),a(s,y)) , Marked_a(a(a(div2,x),a(s,y)),y)>
  <Marked_a(a(divides,a(s,x)),a(s,y)) , Marked_a(a(div2,x),a(s,y))> 
     --> <Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(a(filter,
                                                      a(not,a(divides,x))),
                                             xs)>
  <Marked_a(a(divides,a(s,x)),a(s,y)) , Marked_a(a(div2,x),a(s,y))> 
     --> <Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(sieve,
                                             a(a(filter,a(not,a(divides,x))),
                                              xs))>
  <Marked_a(a(divides,a(s,x)),a(s,y)) , Marked_a(a(div2,x),a(s,y))> 
     --> <Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(a(cons,x),
                                             a(sieve,
                                              a(a(filter,a(not,a(divides,x))),
                                               xs)))>
  <Marked_a(a(divides,a(s,x)),a(s,y)) , Marked_a(a(div2,x),a(s,y))> 
     --> <Marked_a(a(not,f),x) , Marked_a(f,x)>
  <Marked_a(a(divides,a(s,x)),a(s,y)) , Marked_a(a(div2,x),a(s,y))> 
     --> <Marked_a(a(a(if,true),x),xs) , Marked_a(a(cons,x),xs)>
  <Marked_a(a(divides,a(s,x)),a(s,y)) , Marked_a(a(div2,x),a(s,y))> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(filter,f),xs)>
  <Marked_a(a(divides,a(s,x)),a(s,y)) , Marked_a(a(div2,x),a(s,y))> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(f,x)>
  <Marked_a(a(divides,a(s,x)),a(s,y)) , Marked_a(a(div2,x),a(s,y))> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(if,a(f,x)),x)>
  <Marked_a(a(divides,a(s,x)),a(s,y)) , Marked_a(a(div2,x),a(s,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(divides,a(s,x)),a(s,y)) , Marked_a(a(div2,x),a(s,y))> 
     --> <Marked_a(a(a(div2,a(s,x)),y),a(s,z)) , Marked_a(a(div2,x),y)>
  <Marked_a(a(divides,a(s,x)),a(s,y)) , Marked_a(a(div2,x),a(s,y))> 
     --> <Marked_a(a(a(div2,a(s,x)),y),a(s,z)) , Marked_a(a(a(div2,x),y),z)>
  <Marked_a(a(divides,a(s,x)),a(s,y)) , Marked_a(a(div2,x),a(s,y))> 
     --> <Marked_a(a(a(div2,x),y),0) , Marked_a(a(divides,x),y)>
  <Marked_a(a(divides,a(s,x)),a(s,y)) , Marked_a(a(div2,x),a(s,y))> 
     --> <Marked_a(a(divides,a(s,x)),a(s,y)) , Marked_a(a(div2,x),a(s,y))>
  <Marked_a(a(divides,a(s,x)),a(s,y)) , Marked_a(a(div2,x),a(s,y))> 
     --> <Marked_a(a(divides,a(s,x)),a(s,y)) , Marked_a(a(a(div2,x),a(s,y)),y)>
  <Marked_a(a(divides,a(s,x)),a(s,y)) , Marked_a(a(a(div2,x),a(s,y)),y)> 
     --> <Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(a(filter,
                                                      a(not,a(divides,x))),
                                             xs)>
  <Marked_a(a(divides,a(s,x)),a(s,y)) , Marked_a(a(a(div2,x),a(s,y)),y)> 
     --> <Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(sieve,
                                             a(a(filter,a(not,a(divides,x))),
                                              xs))>
  <Marked_a(a(divides,a(s,x)),a(s,y)) , Marked_a(a(a(div2,x),a(s,y)),y)> 
     --> <Marked_a(sieve,a(a(cons,x),xs)) , Marked_a(a(cons,x),
                                             a(sieve,
                                              a(a(filter,a(not,a(divides,x))),
                                               xs)))>
  <Marked_a(a(divides,a(s,x)),a(s,y)) , Marked_a(a(a(div2,x),a(s,y)),y)> 
     --> <Marked_a(a(not,f),x) , Marked_a(f,x)>
  <Marked_a(a(divides,a(s,x)),a(s,y)) , Marked_a(a(a(div2,x),a(s,y)),y)> 
     --> <Marked_a(a(a(if,true),x),xs) , Marked_a(a(cons,x),xs)>
  <Marked_a(a(divides,a(s,x)),a(s,y)) , Marked_a(a(a(div2,x),a(s,y)),y)> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(filter,f),xs)>
  <Marked_a(a(divides,a(s,x)),a(s,y)) , Marked_a(a(a(div2,x),a(s,y)),y)> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(f,x)>
  <Marked_a(a(divides,a(s,x)),a(s,y)) , Marked_a(a(a(div2,x),a(s,y)),y)> 
     --> <Marked_a(a(filter,f),a(a(cons,x),xs)) , Marked_a(a(if,a(f,x)),x)>
  <Marked_a(a(divides,a(s,x)),a(s,y)) , Marked_a(a(a(div2,x),a(s,y)),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(divides,a(s,x)),a(s,y)) , Marked_a(a(a(div2,x),a(s,y)),y)> 
     --> <Marked_a(a(a(div2,a(s,x)),y),a(s,z)) , Marked_a(a(div2,x),y)>
  <Marked_a(a(divides,a(s,x)),a(s,y)) , Marked_a(a(a(div2,x),a(s,y)),y)> 
     --> <Marked_a(a(a(div2,a(s,x)),y),a(s,z)) , Marked_a(a(a(div2,x),y),z)>
  <Marked_a(a(divides,a(s,x)),a(s,y)) , Marked_a(a(a(div2,x),a(s,y)),y)> 
     --> <Marked_a(a(a(div2,x),y),0) , Marked_a(a(divides,x),y)>
  <Marked_a(a(divides,a(s,x)),a(s,y)) , Marked_a(a(a(div2,x),a(s,y)),y)> 
     --> <Marked_a(a(divides,a(s,x)),a(s,y)) , Marked_a(a(div2,x),a(s,y))>
  <Marked_a(a(divides,a(s,x)),a(s,y)) , Marked_a(a(a(div2,x),a(s,y)),y)> 
     --> <Marked_a(a(divides,a(s,x)),a(s,y)) , Marked_a(a(a(div2,x),a(s,y)),y)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  a(a(a(div2,a(s,x)),y),a(s,z)) >= a(a(a(div2,x),y),z) ;
  a(a(a(div2,0),y),a(s,z)) >= false ;
  a(a(a(div2,x),y),0) >= a(a(divides,x),y) ;
  a(a(a(if,true),x),xs) >= a(a(cons,x),xs) ;
  a(a(a(if,false),x),xs) >= xs ;
  a(a(divides,a(s,x)),a(s,y)) >= a(a(a(div2,x),a(s,y)),y) ;
  a(a(divides,0),a(s,y)) >= true ;
  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(not,f),x) >= a(not2,a(f,x)) ;
  a(not2,true) >= false ;
  a(not2,false) >= true ;
  a(sieve,a(a(cons,x),xs)) >= a(a(cons,x),
                               a(sieve,a(a(filter,a(not,a(divides,x))),xs))) ;
  a(sieve,nil) >= nil ;
  Marked_a(a(a(div2,a(s,x)),y),a(s,z)) >= Marked_a(a(a(div2,x),y),z) ;
  Marked_a(a(a(div2,a(s,x)),y),a(s,z)) >= Marked_a(a(div2,x),y) ;
  Marked_a(a(a(div2,x),y),0) >= Marked_a(a(divides,x),y) ;
  Marked_a(a(a(if,true),x),xs) >= Marked_a(a(cons,x),xs) ;
  Marked_a(a(divides,a(s,x)),a(s,y)) >= Marked_a(a(a(div2,x),a(s,y)),y) ;
  Marked_a(a(divides,a(s,x)),a(s,y)) >= Marked_a(a(div2,x),a(s,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(if,a(f,x)),x) ;
  Marked_a(a(filter,f),a(a(cons,x),xs)) >= Marked_a(f,x) ;
  Marked_a(a(not,f),x) >= Marked_a(f,x) ;
  Marked_a(sieve,a(a(cons,x),xs)) >= Marked_a(a(filter,a(not,a(divides,x))),xs) ;
  Marked_a(sieve,a(a(cons,x),xs)) >= Marked_a(a(cons,x),
                                      a(sieve,
                                       a(a(filter,a(not,a(divides,x))),xs))) ;
  Marked_a(sieve,a(a(cons,x),xs)) >= Marked_a(sieve,
                                      a(a(filter,a(not,a(divides,x))),xs)) ;
 }
 + Disjunctions:{ 
{
  Marked_a(a(a(div2,a(s,x)),y),a(s,z)) > Marked_a(a(a(div2,x),y),z) ;
 }
{
  Marked_a(a(a(div2,a(s,x)),y),a(s,z)) > Marked_a(a(div2,x),y) ;
 }
{
  Marked_a(a(a(div2,x),y),0) > Marked_a(a(divides,x),y) ;
 }
{
  Marked_a(a(a(if,true),x),xs) > Marked_a(a(cons,x),xs) ;
 }
{
  Marked_a(a(divides,a(s,x)),a(s,y)) > Marked_a(a(a(div2,x),a(s,y)),y) ;
 }
{
  Marked_a(a(divides,a(s,x)),a(s,y)) > Marked_a(a(div2,x),a(s,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(if,a(f,x)),x) ;
 }
{
  Marked_a(a(filter,f),a(a(cons,x),xs)) > Marked_a(f,x) ;
 }
{
  Marked_a(a(not,f),x) > Marked_a(f,x) ;
 }
{
  Marked_a(sieve,a(a(cons,x),xs)) > Marked_a(a(filter,a(not,a(divides,x))),xs) ;
 }
{
  Marked_a(sieve,a(a(cons,x),xs)) > Marked_a(a(cons,x),
                                     a(sieve,
                                      a(a(filter,a(not,a(divides,x))),xs))) ;
 }
{
  Marked_a(sieve,a(a(cons,x),xs)) > Marked_a(sieve,
                                     a(a(filter,a(not,a(divides,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 : 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 (ID_CRIT)
NOT SOLVED
No proof found
Cime worked for 103.846740 seconds (real time)
Cime Exit Status: 0