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

TRS termination of:
[1] is_empty(nil) -> true
[2] is_empty(cons(x,l)) -> false
[3] hd(cons(x,l)) -> x
[4] tl(cons(x,l)) -> l
[5] append(l1,l2) -> ifappend(l1,l2,l1)
[6] ifappend(l1,l2,nil) -> l2
[7] ifappend(l1,l2,cons(x,l)) -> cons(x,append(l,l2))


Sub problem: 
guided: 

DP termination of:
<Marked_append(l1,l2) , Marked_ifappend(l1,l2,l1)>
<Marked_ifappend(l1,l2,cons(x,l)) , Marked_append(l,l2)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_ifappend(l1,l2,cons(x,l)) , Marked_append(l,l2)> 
      --> <Marked_append(l1,l2) , Marked_ifappend(l1,l2,l1)>
  <Marked_append(l1,l2) , Marked_ifappend(l1,l2,l1)> 
     --> <Marked_ifappend(l1,l2,cons(x,l)) , Marked_append(l,l2)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  is_empty(nil) >= true ;
  is_empty(cons(x,l)) >= false ;
  hd(cons(x,l)) >= x ;
  tl(cons(x,l)) >= l ;
  ifappend(l1,l2,nil) >= l2 ;
  ifappend(l1,l2,cons(x,l)) >= cons(x,append(l,l2)) ;
  append(l1,l2) >= ifappend(l1,l2,l1) ;
  Marked_ifappend(l1,l2,cons(x,l)) >= Marked_append(l,l2) ;
  Marked_append(l1,l2) >= Marked_ifappend(l1,l2,l1) ;
 }
 + Disjunctions:{ 
{
  Marked_ifappend(l1,l2,cons(x,l)) > Marked_append(l,l2) ;
 }
{
  Marked_append(l1,l2) > Marked_ifappend(l1,l2,l1) ;
 }
 } 
=== 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
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: is_empty(nil) >= true
constraint: is_empty(cons(x,l)) >= false
constraint: hd(cons(x,l)) >= x
constraint: tl(cons(x,l)) >= l
constraint: ifappend(l1,l2,nil) >= l2
constraint: ifappend(l1,l2,cons(x,l)) >= cons(x,append(l,l2))
constraint: append(l1,l2) >= ifappend(l1,l2,l1)
constraint: Marked_ifappend(l1,l2,cons(x,l)) >= Marked_append(l,l2)
constraint: Marked_append(l1,l2) >= Marked_ifappend(l1,l2,l1)
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] is_empty(nil) -> true
[2] is_empty(cons(x,l)) -> false
[3] hd(cons(x,l)) -> x
[4] tl(cons(x,l)) -> l
[5] append(l1,l2) -> ifappend(l1,l2,l1)
[6] ifappend(l1,l2,nil) -> l2
[7] ifappend(l1,l2,cons(x,l)) -> cons(x,append(l,l2))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_append(l1,l2) , Marked_ifappend(l1,l2,l1)>
<Marked_ifappend(l1,l2,cons(x,l)) , Marked_append(l,l2)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_append(l1,l2) , Marked_ifappend(l1,l2,l1)>
<Marked_ifappend(l1,l2,cons(x,l)) , Marked_append(l,l2)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ true ] () = 0; 
 [ append ] (X0,X1) = 2*X0 + 3*X1 + 0; 
 [ cons ] (X0,X1) = 2 + 3*X0 + 1*X1 + 0; 
 [ nil ] () = 3 + 0; 
 [ Marked_append ] (X0,X1) = 3 + 3*X0 + 3*X1 + 0; 
 [ tl ] (X0) = 2 + 3*X0 + 0; 
 [ is_empty ] (X0) = 3 + 3*X0 + 0; 
 [ Marked_ifappend ] (X0,X1,X2) = 2 + 3*X1 + 3*X2 + 0; 
 [ hd ] (X0) = 2 + 3*X0 + 0; 
 [ false ] () = 0; 
 [ ifappend ] (X0,X1,X2) = 3*X1 + 2*X2 + 0; 
 ]} 
 ]} 
 ]} 

Cime worked for 0.023958 seconds (real time)
Cime Exit Status: 0