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

TRS termination of:
[1] min(0,y) -> 0
[2] min(s(x),0) -> 0
[3] min(s(x),s(y)) -> min(x,y)
[4] len(nil) -> 0
[5] len(cons(x,xs)) -> s(len(xs))
[6] sum(x,0) -> x
[7] sum(x,s(y)) -> s(sum(x,y))
[8] le(0,x) -> true
[9] le(s(x),0) -> false
[10] le(s(x),s(y)) -> le(x,y)
[11] take(0,cons(y,ys)) -> y
[12] take(s(x),cons(y,ys)) -> take(x,ys)
[13] addList(x,y) -> if(le(0,min(len(x),len(y))),0,x,y,nil)
[14] if(false,c,x,y,z) -> z
[15] if(true,c,xs,ys,z) ->
 if(le(s(c),min(len(xs),len(ys))),s(c),xs,ys,
  cons(sum(take(c,xs),take(c,ys)),z))


Sub problem: 
guided: 

DP termination of:
<Marked_min(s(x),s(y)) , Marked_min(x,y)>
<Marked_len(cons(x,xs)) , Marked_len(xs)>
<Marked_sum(x,s(y)) , Marked_sum(x,y)>
<Marked_le(s(x),s(y)) , Marked_le(x,y)>
<Marked_take(s(x),cons(y,ys)) , Marked_take(x,ys)>
<Marked_addList(x,y) , Marked_if(le(0,min(len(x),len(y))),0,x,y,nil)>
<Marked_addList(x,y) , Marked_le(0,min(len(x),len(y)))>
<Marked_addList(x,y) , Marked_min(len(x),len(y))>
<Marked_addList(x,y) , Marked_len(x)>
<Marked_addList(x,y) , Marked_len(y)>
<Marked_if(true,c,xs,ys,z) , Marked_if(le(s(c),min(len(xs),len(ys))),
                              s(c),xs,ys,cons(sum(take(c,xs),take(c,ys)),z))>
<Marked_if(true,c,xs,ys,z) , Marked_le(s(c),min(len(xs),len(ys)))>
<Marked_if(true,c,xs,ys,z) , Marked_min(len(xs),len(ys))>
<Marked_if(true,c,xs,ys,z) , Marked_len(xs)>
<Marked_if(true,c,xs,ys,z) , Marked_len(ys)>
<Marked_if(true,c,xs,ys,z) , Marked_sum(take(c,xs),take(c,ys))>
<Marked_if(true,c,xs,ys,z) , Marked_take(c,xs)>
<Marked_if(true,c,xs,ys,z) , Marked_take(c,ys)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 6 components:

{  <Marked_if(true,c,xs,ys,z) , Marked_if(le(s(c),min(len(xs),len(ys))),
                                 s(c),xs,ys,cons(sum(take(c,xs),take(c,ys)),z))> 
      --> <Marked_if(true,c,xs,ys,z) , Marked_if(le(s(c),min(len(xs),len(ys))),
                                        s(c),xs,ys,
                                        cons(sum(take(c,xs),take(c,ys)),z))>
}

{  <Marked_le(s(x),s(y)) , Marked_le(x,y)> 
      --> <Marked_le(s(x),s(y)) , Marked_le(x,y)>
}

{  <Marked_min(s(x),s(y)) , Marked_min(x,y)> 
      --> <Marked_min(s(x),s(y)) , Marked_min(x,y)>
}

{  <Marked_len(cons(x,xs)) , Marked_len(xs)> 
      --> <Marked_len(cons(x,xs)) , Marked_len(xs)>
}

{  <Marked_sum(x,s(y)) , Marked_sum(x,y)> 
      --> <Marked_sum(x,s(y)) , Marked_sum(x,y)>
}

{  <Marked_take(s(x),cons(y,ys)) , Marked_take(x,ys)> 
      --> <Marked_take(s(x),cons(y,ys)) , Marked_take(x,ys)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  min(0,y) >= 0 ;
  min(s(x),0) >= 0 ;
  min(s(x),s(y)) >= min(x,y) ;
  len(nil) >= 0 ;
  len(cons(x,xs)) >= s(len(xs)) ;
  sum(x,0) >= x ;
  sum(x,s(y)) >= s(sum(x,y)) ;
  le(0,x) >= true ;
  le(s(x),0) >= false ;
  le(s(x),s(y)) >= le(x,y) ;
  take(0,cons(y,ys)) >= y ;
  take(s(x),cons(y,ys)) >= take(x,ys) ;
  if(true,c,xs,ys,z) >= if(le(s(c),min(len(xs),len(ys))),s(c),xs,ys,
                         cons(sum(take(c,xs),take(c,ys)),z)) ;
  if(false,c,x,y,z) >= z ;
  addList(x,y) >= if(le(0,min(len(x),len(y))),0,x,y,nil) ;
  Marked_if(true,c,xs,ys,z) >= Marked_if(le(s(c),min(len(xs),len(ys))),
                                s(c),xs,ys,cons(sum(take(c,xs),take(c,ys)),z)) ;
 }
 + Disjunctions:{ 
{
  Marked_if(true,c,xs,ys,z) > Marked_if(le(s(c),min(len(xs),len(ys))),
                               s(c),xs,ys,cons(sum(take(c,xs),take(c,ys)),z)) ;
 }
 } 
=== 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 : 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
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 22.301865 seconds (real time)
Cime Exit Status: 0