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

TRS termination of:
[1] ap(ap(map,f),xs) -> ap(ap(ap(if,ap(isEmpty,xs)),f),xs)
[2] ap(ap(ap(if,true),f),xs) -> null
[3] ap(ap(ap(if,null),f),xs) -> ap(ap(cons,ap(f,ap(last,xs))),ap(ap(if2,f),xs))
[4] ap(ap(if2,f),xs) -> ap(ap(map,f),ap(dropLast,xs))
[5] ap(isEmpty,null) -> true
[6] ap(isEmpty,ap(ap(cons,x),xs)) -> null
[7] ap(last,ap(ap(cons,x),null)) -> x
[8] ap(last,ap(ap(cons,x),ap(ap(cons,y),ys))) -> ap(last,ap(ap(cons,y),ys))
[9] ap(dropLast,ap(ap(cons,x),null)) -> null
[10] ap(dropLast,ap(ap(cons,x),ap(ap(cons,y),ys))) ->
 ap(ap(cons,x),ap(dropLast,ap(ap(cons,y),ys)))


Sub problem: 
guided: 

DP termination of:
<Marked_ap(ap(map,f),xs) , Marked_ap(ap(ap(if,ap(isEmpty,xs)),f),xs)>
<Marked_ap(ap(map,f),xs) , Marked_ap(ap(if,ap(isEmpty,xs)),f)>
<Marked_ap(ap(map,f),xs) , Marked_ap(if,ap(isEmpty,xs))>
<Marked_ap(ap(map,f),xs) , Marked_ap(isEmpty,xs)>
<Marked_ap(ap(ap(if,null),f),xs) , Marked_ap(ap(cons,ap(f,ap(last,xs))),
                                    ap(ap(if2,f),xs))>
<Marked_ap(ap(ap(if,null),f),xs) , Marked_ap(cons,ap(f,ap(last,xs)))>
<Marked_ap(ap(ap(if,null),f),xs) , Marked_ap(f,ap(last,xs))>
<Marked_ap(ap(ap(if,null),f),xs) , Marked_ap(last,xs)>
<Marked_ap(ap(ap(if,null),f),xs) , Marked_ap(ap(if2,f),xs)>
<Marked_ap(ap(ap(if,null),f),xs) , Marked_ap(if2,f)>
<Marked_ap(ap(if2,f),xs) , Marked_ap(ap(map,f),ap(dropLast,xs))>
<Marked_ap(ap(if2,f),xs) , Marked_ap(map,f)>
<Marked_ap(ap(if2,f),xs) , Marked_ap(dropLast,xs)>
<Marked_ap(last,ap(ap(cons,x),ap(ap(cons,y),ys))) , Marked_ap(last,
                                                     ap(ap(cons,y),ys))>
<Marked_ap(dropLast,ap(ap(cons,x),ap(ap(cons,y),ys))) , Marked_ap(ap(cons,x),
                                                         ap(dropLast,
                                                          ap(ap(cons,y),ys)))>
<Marked_ap(dropLast,ap(ap(cons,x),ap(ap(cons,y),ys))) , Marked_ap(dropLast,
                                                         ap(ap(cons,y),ys))>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <Marked_ap(dropLast,ap(ap(cons,x),ap(ap(cons,y),ys))) , Marked_ap(
                                                            dropLast,
                                                            ap(ap(cons,y),ys))> 
      --> <Marked_ap(dropLast,ap(ap(cons,x),ap(ap(cons,y),ys))) , Marked_ap(
                                                                   dropLast,
                                                                   ap(
                                                                    ap(
                                                                    cons,
                                                                    y),
                                                                    ys))>
  <Marked_ap(dropLast,ap(ap(cons,x),ap(ap(cons,y),ys))) , Marked_ap(dropLast,
                                                           ap(ap(cons,y),ys))> 
     --> <Marked_ap(dropLast,ap(ap(cons,x),ap(ap(cons,y),ys))) , Marked_ap(
                                                                  ap(
                                                                   cons,
                                                                   x),
                                                                  ap(
                                                                   dropLast,
                                                                   ap(
                                                                    ap(
                                                                    cons,
                                                                    y),
                                                                    ys)))>
  <Marked_ap(dropLast,ap(ap(cons,x),ap(ap(cons,y),ys))) , Marked_ap(ap(cons,x),
                                                           ap(dropLast,
                                                            ap(ap(cons,y),ys)))> 
     --> <Marked_ap(dropLast,ap(ap(cons,x),ap(ap(cons,y),ys))) , Marked_ap(
                                                                  dropLast,
                                                                  ap(
                                                                   ap(cons,y),
                                                                   ys))>
  <Marked_ap(dropLast,ap(ap(cons,x),ap(ap(cons,y),ys))) , Marked_ap(ap(cons,x),
                                                           ap(dropLast,
                                                            ap(ap(cons,y),ys)))> 
     --> <Marked_ap(dropLast,ap(ap(cons,x),ap(ap(cons,y),ys))) , Marked_ap(
                                                                  ap(
                                                                   cons,
                                                                   x),
                                                                  ap(
                                                                   dropLast,
                                                                   ap(
                                                                    ap(
                                                                    cons,
                                                                    y),
                                                                    ys)))>
  <Marked_ap(dropLast,ap(ap(cons,x),ap(ap(cons,y),ys))) , Marked_ap(ap(cons,x),
                                                           ap(dropLast,
                                                            ap(ap(cons,y),ys)))> 
     --> <Marked_ap(ap(if2,f),xs) , Marked_ap(dropLast,xs)>
  <Marked_ap(dropLast,ap(ap(cons,x),ap(ap(cons,y),ys))) , Marked_ap(ap(cons,x),
                                                           ap(dropLast,
                                                            ap(ap(cons,y),ys)))> 
     --> <Marked_ap(ap(if2,f),xs) , Marked_ap(ap(map,f),ap(dropLast,xs))>
  <Marked_ap(dropLast,ap(ap(cons,x),ap(ap(cons,y),ys))) , Marked_ap(ap(cons,x),
                                                           ap(dropLast,
                                                            ap(ap(cons,y),ys)))> 
     --> <Marked_ap(ap(ap(if,null),f),xs) , Marked_ap(ap(if2,f),xs)>
  <Marked_ap(dropLast,ap(ap(cons,x),ap(ap(cons,y),ys))) , Marked_ap(ap(cons,x),
                                                           ap(dropLast,
                                                            ap(ap(cons,y),ys)))> 
     --> <Marked_ap(ap(ap(if,null),f),xs) , Marked_ap(f,ap(last,xs))>
  <Marked_ap(dropLast,ap(ap(cons,x),ap(ap(cons,y),ys))) , Marked_ap(ap(cons,x),
                                                           ap(dropLast,
                                                            ap(ap(cons,y),ys)))> 
     --> <Marked_ap(ap(ap(if,null),f),xs) , Marked_ap(ap(cons,
                                                       ap(f,ap(last,xs))),
                                             ap(ap(if2,f),xs))>
  <Marked_ap(dropLast,ap(ap(cons,x),ap(ap(cons,y),ys))) , Marked_ap(ap(cons,x),
                                                           ap(dropLast,
                                                            ap(ap(cons,y),ys)))> 
     --> <Marked_ap(ap(map,f),xs) , Marked_ap(ap(if,ap(isEmpty,xs)),f)>
  <Marked_ap(dropLast,ap(ap(cons,x),ap(ap(cons,y),ys))) , Marked_ap(ap(cons,x),
                                                           ap(dropLast,
                                                            ap(ap(cons,y),ys)))> 
     --> <Marked_ap(ap(map,f),xs) , Marked_ap(ap(ap(if,ap(isEmpty,xs)),f),xs)>
  <Marked_ap(ap(if2,f),xs) , Marked_ap(dropLast,xs)> 
     --> <Marked_ap(dropLast,ap(ap(cons,x),ap(ap(cons,y),ys))) , Marked_ap(
                                                                  dropLast,
                                                                  ap(
                                                                   ap(cons,y),
                                                                   ys))>
  <Marked_ap(ap(if2,f),xs) , Marked_ap(dropLast,xs)> 
     --> <Marked_ap(dropLast,ap(ap(cons,x),ap(ap(cons,y),ys))) , Marked_ap(
                                                                  ap(
                                                                   cons,
                                                                   x),
                                                                  ap(
                                                                   dropLast,
                                                                   ap(
                                                                    ap(
                                                                    cons,
                                                                    y),
                                                                    ys)))>
  <Marked_ap(ap(if2,f),xs) , Marked_ap(ap(map,f),ap(dropLast,xs))> 
     --> <Marked_ap(dropLast,ap(ap(cons,x),ap(ap(cons,y),ys))) , Marked_ap(
                                                                  dropLast,
                                                                  ap(
                                                                   ap(cons,y),
                                                                   ys))>
  <Marked_ap(ap(if2,f),xs) , Marked_ap(ap(map,f),ap(dropLast,xs))> 
     --> <Marked_ap(dropLast,ap(ap(cons,x),ap(ap(cons,y),ys))) , Marked_ap(
                                                                  ap(
                                                                   cons,
                                                                   x),
                                                                  ap(
                                                                   dropLast,
                                                                   ap(
                                                                    ap(
                                                                    cons,
                                                                    y),
                                                                    ys)))>
  <Marked_ap(ap(if2,f),xs) , Marked_ap(ap(map,f),ap(dropLast,xs))> 
     --> <Marked_ap(ap(if2,f),xs) , Marked_ap(dropLast,xs)>
  <Marked_ap(ap(if2,f),xs) , Marked_ap(ap(map,f),ap(dropLast,xs))> 
     --> <Marked_ap(ap(if2,f),xs) , Marked_ap(ap(map,f),ap(dropLast,xs))>
  <Marked_ap(ap(if2,f),xs) , Marked_ap(ap(map,f),ap(dropLast,xs))> 
     --> <Marked_ap(ap(ap(if,null),f),xs) , Marked_ap(ap(if2,f),xs)>
  <Marked_ap(ap(if2,f),xs) , Marked_ap(ap(map,f),ap(dropLast,xs))> 
     --> <Marked_ap(ap(ap(if,null),f),xs) , Marked_ap(f,ap(last,xs))>
  <Marked_ap(ap(if2,f),xs) , Marked_ap(ap(map,f),ap(dropLast,xs))> 
     --> <Marked_ap(ap(ap(if,null),f),xs) , Marked_ap(ap(cons,
                                                       ap(f,ap(last,xs))),
                                             ap(ap(if2,f),xs))>
  <Marked_ap(ap(if2,f),xs) , Marked_ap(ap(map,f),ap(dropLast,xs))> 
     --> <Marked_ap(ap(map,f),xs) , Marked_ap(ap(if,ap(isEmpty,xs)),f)>
  <Marked_ap(ap(if2,f),xs) , Marked_ap(ap(map,f),ap(dropLast,xs))> 
     --> <Marked_ap(ap(map,f),xs) , Marked_ap(ap(ap(if,ap(isEmpty,xs)),f),xs)>
  <Marked_ap(ap(ap(if,null),f),xs) , Marked_ap(ap(if2,f),xs)> 
     --> <Marked_ap(dropLast,ap(ap(cons,x),ap(ap(cons,y),ys))) , Marked_ap(
                                                                  dropLast,
                                                                  ap(
                                                                   ap(cons,y),
                                                                   ys))>
  <Marked_ap(ap(ap(if,null),f),xs) , Marked_ap(ap(if2,f),xs)> 
     --> <Marked_ap(dropLast,ap(ap(cons,x),ap(ap(cons,y),ys))) , Marked_ap(
                                                                  ap(
                                                                   cons,
                                                                   x),
                                                                  ap(
                                                                   dropLast,
                                                                   ap(
                                                                    ap(
                                                                    cons,
                                                                    y),
                                                                    ys)))>
  <Marked_ap(ap(ap(if,null),f),xs) , Marked_ap(ap(if2,f),xs)> 
     --> <Marked_ap(ap(if2,f),xs) , Marked_ap(dropLast,xs)>
  <Marked_ap(ap(ap(if,null),f),xs) , Marked_ap(ap(if2,f),xs)> 
     --> <Marked_ap(ap(if2,f),xs) , Marked_ap(ap(map,f),ap(dropLast,xs))>
  <Marked_ap(ap(ap(if,null),f),xs) , Marked_ap(ap(if2,f),xs)> 
     --> <Marked_ap(ap(ap(if,null),f),xs) , Marked_ap(ap(if2,f),xs)>
  <Marked_ap(ap(ap(if,null),f),xs) , Marked_ap(ap(if2,f),xs)> 
     --> <Marked_ap(ap(ap(if,null),f),xs) , Marked_ap(f,ap(last,xs))>
  <Marked_ap(ap(ap(if,null),f),xs) , Marked_ap(ap(if2,f),xs)> 
     --> <Marked_ap(ap(ap(if,null),f),xs) , Marked_ap(ap(cons,
                                                       ap(f,ap(last,xs))),
                                             ap(ap(if2,f),xs))>
  <Marked_ap(ap(ap(if,null),f),xs) , Marked_ap(ap(if2,f),xs)> 
     --> <Marked_ap(ap(map,f),xs) , Marked_ap(ap(if,ap(isEmpty,xs)),f)>
  <Marked_ap(ap(ap(if,null),f),xs) , Marked_ap(ap(if2,f),xs)> 
     --> <Marked_ap(ap(map,f),xs) , Marked_ap(ap(ap(if,ap(isEmpty,xs)),f),xs)>
  <Marked_ap(ap(ap(if,null),f),xs) , Marked_ap(f,ap(last,xs))> 
     --> <Marked_ap(dropLast,ap(ap(cons,x),ap(ap(cons,y),ys))) , Marked_ap(
                                                                  dropLast,
                                                                  ap(
                                                                   ap(cons,y),
                                                                   ys))>
  <Marked_ap(ap(ap(if,null),f),xs) , Marked_ap(f,ap(last,xs))> 
     --> <Marked_ap(dropLast,ap(ap(cons,x),ap(ap(cons,y),ys))) , Marked_ap(
                                                                  ap(
                                                                   cons,
                                                                   x),
                                                                  ap(
                                                                   dropLast,
                                                                   ap(
                                                                    ap(
                                                                    cons,
                                                                    y),
                                                                    ys)))>
  <Marked_ap(ap(ap(if,null),f),xs) , Marked_ap(f,ap(last,xs))> 
     --> <Marked_ap(ap(if2,f),xs) , Marked_ap(dropLast,xs)>
  <Marked_ap(ap(ap(if,null),f),xs) , Marked_ap(f,ap(last,xs))> 
     --> <Marked_ap(ap(if2,f),xs) , Marked_ap(ap(map,f),ap(dropLast,xs))>
  <Marked_ap(ap(ap(if,null),f),xs) , Marked_ap(f,ap(last,xs))> 
     --> <Marked_ap(ap(ap(if,null),f),xs) , Marked_ap(ap(if2,f),xs)>
  <Marked_ap(ap(ap(if,null),f),xs) , Marked_ap(f,ap(last,xs))> 
     --> <Marked_ap(ap(ap(if,null),f),xs) , Marked_ap(f,ap(last,xs))>
  <Marked_ap(ap(ap(if,null),f),xs) , Marked_ap(f,ap(last,xs))> 
     --> <Marked_ap(ap(ap(if,null),f),xs) , Marked_ap(ap(cons,
                                                       ap(f,ap(last,xs))),
                                             ap(ap(if2,f),xs))>
  <Marked_ap(ap(ap(if,null),f),xs) , Marked_ap(f,ap(last,xs))> 
     --> <Marked_ap(ap(map,f),xs) , Marked_ap(ap(if,ap(isEmpty,xs)),f)>
  <Marked_ap(ap(ap(if,null),f),xs) , Marked_ap(f,ap(last,xs))> 
     --> <Marked_ap(ap(map,f),xs) , Marked_ap(ap(ap(if,ap(isEmpty,xs)),f),xs)>
  <Marked_ap(ap(ap(if,null),f),xs) , Marked_ap(ap(cons,ap(f,ap(last,xs))),
                                      ap(ap(if2,f),xs))> 
     --> <Marked_ap(dropLast,ap(ap(cons,x),ap(ap(cons,y),ys))) , Marked_ap(
                                                                  dropLast,
                                                                  ap(
                                                                   ap(cons,y),
                                                                   ys))>
  <Marked_ap(ap(ap(if,null),f),xs) , Marked_ap(ap(cons,ap(f,ap(last,xs))),
                                      ap(ap(if2,f),xs))> 
     --> <Marked_ap(dropLast,ap(ap(cons,x),ap(ap(cons,y),ys))) , Marked_ap(
                                                                  ap(
                                                                   cons,
                                                                   x),
                                                                  ap(
                                                                   dropLast,
                                                                   ap(
                                                                    ap(
                                                                    cons,
                                                                    y),
                                                                    ys)))>
  <Marked_ap(ap(ap(if,null),f),xs) , Marked_ap(ap(cons,ap(f,ap(last,xs))),
                                      ap(ap(if2,f),xs))> 
     --> <Marked_ap(ap(if2,f),xs) , Marked_ap(dropLast,xs)>
  <Marked_ap(ap(ap(if,null),f),xs) , Marked_ap(ap(cons,ap(f,ap(last,xs))),
                                      ap(ap(if2,f),xs))> 
     --> <Marked_ap(ap(if2,f),xs) , Marked_ap(ap(map,f),ap(dropLast,xs))>
  <Marked_ap(ap(ap(if,null),f),xs) , Marked_ap(ap(cons,ap(f,ap(last,xs))),
                                      ap(ap(if2,f),xs))> 
     --> <Marked_ap(ap(ap(if,null),f),xs) , Marked_ap(ap(if2,f),xs)>
  <Marked_ap(ap(ap(if,null),f),xs) , Marked_ap(ap(cons,ap(f,ap(last,xs))),
                                      ap(ap(if2,f),xs))> 
     --> <Marked_ap(ap(ap(if,null),f),xs) , Marked_ap(f,ap(last,xs))>
  <Marked_ap(ap(ap(if,null),f),xs) , Marked_ap(ap(cons,ap(f,ap(last,xs))),
                                      ap(ap(if2,f),xs))> 
     --> <Marked_ap(ap(ap(if,null),f),xs) , Marked_ap(ap(cons,
                                                       ap(f,ap(last,xs))),
                                             ap(ap(if2,f),xs))>
  <Marked_ap(ap(ap(if,null),f),xs) , Marked_ap(ap(cons,ap(f,ap(last,xs))),
                                      ap(ap(if2,f),xs))> 
     --> <Marked_ap(ap(map,f),xs) , Marked_ap(ap(if,ap(isEmpty,xs)),f)>
  <Marked_ap(ap(ap(if,null),f),xs) , Marked_ap(ap(cons,ap(f,ap(last,xs))),
                                      ap(ap(if2,f),xs))> 
     --> <Marked_ap(ap(map,f),xs) , Marked_ap(ap(ap(if,ap(isEmpty,xs)),f),xs)>
  <Marked_ap(ap(map,f),xs) , Marked_ap(ap(if,ap(isEmpty,xs)),f)> 
     --> <Marked_ap(dropLast,ap(ap(cons,x),ap(ap(cons,y),ys))) , Marked_ap(
                                                                  dropLast,
                                                                  ap(
                                                                   ap(cons,y),
                                                                   ys))>
  <Marked_ap(ap(map,f),xs) , Marked_ap(ap(if,ap(isEmpty,xs)),f)> 
     --> <Marked_ap(dropLast,ap(ap(cons,x),ap(ap(cons,y),ys))) , Marked_ap(
                                                                  ap(
                                                                   cons,
                                                                   x),
                                                                  ap(
                                                                   dropLast,
                                                                   ap(
                                                                    ap(
                                                                    cons,
                                                                    y),
                                                                    ys)))>
  <Marked_ap(ap(map,f),xs) , Marked_ap(ap(if,ap(isEmpty,xs)),f)> 
     --> <Marked_ap(ap(if2,f),xs) , Marked_ap(dropLast,xs)>
  <Marked_ap(ap(map,f),xs) , Marked_ap(ap(if,ap(isEmpty,xs)),f)> 
     --> <Marked_ap(ap(if2,f),xs) , Marked_ap(ap(map,f),ap(dropLast,xs))>
  <Marked_ap(ap(map,f),xs) , Marked_ap(ap(if,ap(isEmpty,xs)),f)> 
     --> <Marked_ap(ap(ap(if,null),f),xs) , Marked_ap(ap(if2,f),xs)>
  <Marked_ap(ap(map,f),xs) , Marked_ap(ap(if,ap(isEmpty,xs)),f)> 
     --> <Marked_ap(ap(ap(if,null),f),xs) , Marked_ap(f,ap(last,xs))>
  <Marked_ap(ap(map,f),xs) , Marked_ap(ap(if,ap(isEmpty,xs)),f)> 
     --> <Marked_ap(ap(ap(if,null),f),xs) , Marked_ap(ap(cons,
                                                       ap(f,ap(last,xs))),
                                             ap(ap(if2,f),xs))>
  <Marked_ap(ap(map,f),xs) , Marked_ap(ap(if,ap(isEmpty,xs)),f)> 
     --> <Marked_ap(ap(map,f),xs) , Marked_ap(ap(if,ap(isEmpty,xs)),f)>
  <Marked_ap(ap(map,f),xs) , Marked_ap(ap(if,ap(isEmpty,xs)),f)> 
     --> <Marked_ap(ap(map,f),xs) , Marked_ap(ap(ap(if,ap(isEmpty,xs)),f),xs)>
  <Marked_ap(ap(map,f),xs) , Marked_ap(ap(ap(if,ap(isEmpty,xs)),f),xs)> 
     --> <Marked_ap(dropLast,ap(ap(cons,x),ap(ap(cons,y),ys))) , Marked_ap(
                                                                  dropLast,
                                                                  ap(
                                                                   ap(cons,y),
                                                                   ys))>
  <Marked_ap(ap(map,f),xs) , Marked_ap(ap(ap(if,ap(isEmpty,xs)),f),xs)> 
     --> <Marked_ap(dropLast,ap(ap(cons,x),ap(ap(cons,y),ys))) , Marked_ap(
                                                                  ap(
                                                                   cons,
                                                                   x),
                                                                  ap(
                                                                   dropLast,
                                                                   ap(
                                                                    ap(
                                                                    cons,
                                                                    y),
                                                                    ys)))>
  <Marked_ap(ap(map,f),xs) , Marked_ap(ap(ap(if,ap(isEmpty,xs)),f),xs)> 
     --> <Marked_ap(ap(if2,f),xs) , Marked_ap(dropLast,xs)>
  <Marked_ap(ap(map,f),xs) , Marked_ap(ap(ap(if,ap(isEmpty,xs)),f),xs)> 
     --> <Marked_ap(ap(if2,f),xs) , Marked_ap(ap(map,f),ap(dropLast,xs))>
  <Marked_ap(ap(map,f),xs) , Marked_ap(ap(ap(if,ap(isEmpty,xs)),f),xs)> 
     --> <Marked_ap(ap(ap(if,null),f),xs) , Marked_ap(ap(if2,f),xs)>
  <Marked_ap(ap(map,f),xs) , Marked_ap(ap(ap(if,ap(isEmpty,xs)),f),xs)> 
     --> <Marked_ap(ap(ap(if,null),f),xs) , Marked_ap(f,ap(last,xs))>
  <Marked_ap(ap(map,f),xs) , Marked_ap(ap(ap(if,ap(isEmpty,xs)),f),xs)> 
     --> <Marked_ap(ap(ap(if,null),f),xs) , Marked_ap(ap(cons,
                                                       ap(f,ap(last,xs))),
                                             ap(ap(if2,f),xs))>
  <Marked_ap(ap(map,f),xs) , Marked_ap(ap(ap(if,ap(isEmpty,xs)),f),xs)> 
     --> <Marked_ap(ap(map,f),xs) , Marked_ap(ap(if,ap(isEmpty,xs)),f)>
  <Marked_ap(ap(map,f),xs) , Marked_ap(ap(ap(if,ap(isEmpty,xs)),f),xs)> 
     --> <Marked_ap(ap(map,f),xs) , Marked_ap(ap(ap(if,ap(isEmpty,xs)),f),xs)>
}

{  <Marked_ap(last,ap(ap(cons,x),ap(ap(cons,y),ys))) , Marked_ap(last,
                                                        ap(ap(cons,y),ys))> 
      --> <Marked_ap(last,ap(ap(cons,x),ap(ap(cons,y),ys))) , Marked_ap(
                                                               last,
                                                               ap(ap(cons,y),
                                                                ys))>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  ap(ap(ap(if,null),f),xs) >= ap(ap(cons,ap(f,ap(last,xs))),ap(ap(if2,f),xs)) ;
  ap(ap(ap(if,true),f),xs) >= null ;
  ap(ap(map,f),xs) >= ap(ap(ap(if,ap(isEmpty,xs)),f),xs) ;
  ap(ap(if2,f),xs) >= ap(ap(map,f),ap(dropLast,xs)) ;
  ap(isEmpty,ap(ap(cons,x),xs)) >= null ;
  ap(isEmpty,null) >= true ;
  ap(last,ap(ap(cons,x),ap(ap(cons,y),ys))) >= ap(last,ap(ap(cons,y),ys)) ;
  ap(last,ap(ap(cons,x),null)) >= x ;
  ap(dropLast,ap(ap(cons,x),ap(ap(cons,y),ys))) >= ap(ap(cons,x),
                                                    ap(dropLast,
                                                     ap(ap(cons,y),ys))) ;
  ap(dropLast,ap(ap(cons,x),null)) >= null ;
  Marked_ap(ap(ap(if,null),f),xs) >= Marked_ap(ap(cons,ap(f,ap(last,xs))),
                                      ap(ap(if2,f),xs)) ;
  Marked_ap(ap(ap(if,null),f),xs) >= Marked_ap(ap(if2,f),xs) ;
  Marked_ap(ap(ap(if,null),f),xs) >= Marked_ap(f,ap(last,xs)) ;
  Marked_ap(ap(map,f),xs) >= Marked_ap(ap(ap(if,ap(isEmpty,xs)),f),xs) ;
  Marked_ap(ap(map,f),xs) >= Marked_ap(ap(if,ap(isEmpty,xs)),f) ;
  Marked_ap(ap(if2,f),xs) >= Marked_ap(ap(map,f),ap(dropLast,xs)) ;
  Marked_ap(ap(if2,f),xs) >= Marked_ap(dropLast,xs) ;
  Marked_ap(dropLast,ap(ap(cons,x),ap(ap(cons,y),ys))) >= Marked_ap(ap(cons,x),
                                                           ap(dropLast,
                                                            ap(ap(cons,y),ys))) ;
  Marked_ap(dropLast,ap(ap(cons,x),ap(ap(cons,y),ys))) >= Marked_ap(dropLast,
                                                           ap(ap(cons,y),ys)) ;
 }
 + Disjunctions:{ 
{
  Marked_ap(ap(ap(if,null),f),xs) > Marked_ap(ap(cons,ap(f,ap(last,xs))),
                                     ap(ap(if2,f),xs)) ;
 }
{
  Marked_ap(ap(ap(if,null),f),xs) > Marked_ap(ap(if2,f),xs) ;
 }
{
  Marked_ap(ap(ap(if,null),f),xs) > Marked_ap(f,ap(last,xs)) ;
 }
{
  Marked_ap(ap(map,f),xs) > Marked_ap(ap(ap(if,ap(isEmpty,xs)),f),xs) ;
 }
{
  Marked_ap(ap(map,f),xs) > Marked_ap(ap(if,ap(isEmpty,xs)),f) ;
 }
{
  Marked_ap(ap(if2,f),xs) > Marked_ap(ap(map,f),ap(dropLast,xs)) ;
 }
{
  Marked_ap(ap(if2,f),xs) > Marked_ap(dropLast,xs) ;
 }
{
  Marked_ap(dropLast,ap(ap(cons,x),ap(ap(cons,y),ys))) > Marked_ap(ap(cons,x),
                                                          ap(dropLast,
                                                           ap(ap(cons,y),ys))) ;
 }
{
  Marked_ap(dropLast,ap(ap(cons,x),ap(ap(cons,y),ys))) > Marked_ap(dropLast,
                                                          ap(ap(cons,y),ys)) ;
 }
 } 
=== 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 : 15.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 15.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
=== TIMER virtual : 50.000000 ===
trying sub matrices of size: 1
Matrix interpretation constraints generated.
Search parameters: LINEAR MATRIX 3x3 (strict=1x1) ; time limit: 50.. 
Termination constraints generated.
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 50.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
No solution found for these constraints.
APPLY CRITERIA (ID_CRIT)
NOT SOLVED
No proof found
Cime worked for 17.025026 seconds (real time)
Cime Exit Status: 0