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

TRS termination of:
[1] a__and(true,X) -> mark(X)
[2] a__and(false,Y) -> false
[3] a__if(true,X,Y) -> mark(X)
[4] a__if(false,X,Y) -> mark(Y)
[5] a__add(0,X) -> mark(X)
[6] a__add(s(X),Y) -> s(add(X,Y))
[7] a__first(0,X) -> nil
[8] a__first(s(X),cons(Y,Z)) -> cons(Y,first(X,Z))
[9] a__from(X) -> cons(X,from(s(X)))
[10] mark(and(X1,X2)) -> a__and(mark(X1),X2)
[11] mark(if(X1,X2,X3)) -> a__if(mark(X1),X2,X3)
[12] mark(add(X1,X2)) -> a__add(mark(X1),X2)
[13] mark(first(X1,X2)) -> a__first(mark(X1),mark(X2))
[14] mark(from(X)) -> a__from(X)
[15] mark(true) -> true
[16] mark(false) -> false
[17] mark(0) -> 0
[18] mark(s(X)) -> s(X)
[19] mark(nil) -> nil
[20] mark(cons(X1,X2)) -> cons(X1,X2)
[21] a__and(X1,X2) -> and(X1,X2)
[22] a__if(X1,X2,X3) -> if(X1,X2,X3)
[23] a__add(X1,X2) -> add(X1,X2)
[24] a__first(X1,X2) -> first(X1,X2)
[25] a__from(X) -> from(X)


Sub problem: 
guided: 

DP termination of:
<Marked_a__and(true,X) , Marked_mark(X)>
<Marked_a__if(true,X,Y) , Marked_mark(X)>
<Marked_a__if(false,X,Y) , Marked_mark(Y)>
<Marked_a__add(0,X) , Marked_mark(X)>
<Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
<Marked_mark(and(X1,X2)) , Marked_mark(X1)>
<Marked_mark(if(X1,X2,X3)) , Marked_a__if(mark(X1),X2,X3)>
<Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)>
<Marked_mark(add(X1,X2)) , Marked_a__add(mark(X1),X2)>
<Marked_mark(add(X1,X2)) , Marked_mark(X1)>
<Marked_mark(first(X1,X2)) , Marked_a__first(mark(X1),mark(X2))>
<Marked_mark(first(X1,X2)) , Marked_mark(X1)>
<Marked_mark(first(X1,X2)) , Marked_mark(X2)>
<Marked_mark(from(X)) , Marked_a__from(X)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_mark(first(X1,X2)) , Marked_mark(X2)> 
      --> <Marked_mark(first(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(first(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(first(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(first(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(add(X1,X2)) , Marked_a__add(mark(X1),X2)>
  <Marked_mark(first(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(first(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_a__if(mark(X1),X2,X3)>
  <Marked_mark(first(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(first(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
  <Marked_mark(first(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(first(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(first(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(first(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(add(X1,X2)) , Marked_a__add(mark(X1),X2)>
  <Marked_mark(first(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(first(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_a__if(mark(X1),X2,X3)>
  <Marked_mark(first(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(first(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
  <Marked_mark(add(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(add(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(add(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(add(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(add(X1,X2)) , Marked_a__add(mark(X1),X2)>
  <Marked_mark(add(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(add(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_a__if(mark(X1),X2,X3)>
  <Marked_mark(add(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(add(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
  <Marked_mark(add(X1,X2)) , Marked_a__add(mark(X1),X2)> 
     --> <Marked_a__add(0,X) , Marked_mark(X)>
  <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(add(X1,X2)) , Marked_a__add(mark(X1),X2)>
  <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_a__if(mark(X1),X2,X3)>
  <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
  <Marked_mark(if(X1,X2,X3)) , Marked_a__if(mark(X1),X2,X3)> 
     --> <Marked_a__if(false,X,Y) , Marked_mark(Y)>
  <Marked_mark(if(X1,X2,X3)) , Marked_a__if(mark(X1),X2,X3)> 
     --> <Marked_a__if(true,X,Y) , Marked_mark(X)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(add(X1,X2)) , Marked_a__add(mark(X1),X2)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_a__if(mark(X1),X2,X3)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
  <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)> 
     --> <Marked_a__and(true,X) , Marked_mark(X)>
  <Marked_a__add(0,X) , Marked_mark(X)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X2)>
  <Marked_a__add(0,X) , Marked_mark(X)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X1)>
  <Marked_a__add(0,X) , Marked_mark(X)> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X1)>
  <Marked_a__add(0,X) , Marked_mark(X)> 
     --> <Marked_mark(add(X1,X2)) , Marked_a__add(mark(X1),X2)>
  <Marked_a__add(0,X) , Marked_mark(X)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_a__add(0,X) , Marked_mark(X)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_a__if(mark(X1),X2,X3)>
  <Marked_a__add(0,X) , Marked_mark(X)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_a__add(0,X) , Marked_mark(X)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
  <Marked_a__if(false,X,Y) , Marked_mark(Y)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X2)>
  <Marked_a__if(false,X,Y) , Marked_mark(Y)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X1)>
  <Marked_a__if(false,X,Y) , Marked_mark(Y)> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X1)>
  <Marked_a__if(false,X,Y) , Marked_mark(Y)> 
     --> <Marked_mark(add(X1,X2)) , Marked_a__add(mark(X1),X2)>
  <Marked_a__if(false,X,Y) , Marked_mark(Y)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_a__if(false,X,Y) , Marked_mark(Y)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_a__if(mark(X1),X2,X3)>
  <Marked_a__if(false,X,Y) , Marked_mark(Y)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_a__if(false,X,Y) , Marked_mark(Y)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
  <Marked_a__if(true,X,Y) , Marked_mark(X)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X2)>
  <Marked_a__if(true,X,Y) , Marked_mark(X)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X1)>
  <Marked_a__if(true,X,Y) , Marked_mark(X)> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X1)>
  <Marked_a__if(true,X,Y) , Marked_mark(X)> 
     --> <Marked_mark(add(X1,X2)) , Marked_a__add(mark(X1),X2)>
  <Marked_a__if(true,X,Y) , Marked_mark(X)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_a__if(true,X,Y) , Marked_mark(X)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_a__if(mark(X1),X2,X3)>
  <Marked_a__if(true,X,Y) , Marked_mark(X)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_a__if(true,X,Y) , Marked_mark(X)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
  <Marked_a__and(true,X) , Marked_mark(X)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X2)>
  <Marked_a__and(true,X) , Marked_mark(X)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X1)>
  <Marked_a__and(true,X) , Marked_mark(X)> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X1)>
  <Marked_a__and(true,X) , Marked_mark(X)> 
     --> <Marked_mark(add(X1,X2)) , Marked_a__add(mark(X1),X2)>
  <Marked_a__and(true,X) , Marked_mark(X)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_a__and(true,X) , Marked_mark(X)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_a__if(mark(X1),X2,X3)>
  <Marked_a__and(true,X) , Marked_mark(X)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_a__and(true,X) , Marked_mark(X)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  mark(true) >= true ;
  mark(false) >= false ;
  mark(0) >= 0 ;
  mark(s(X)) >= s(X) ;
  mark(add(X1,X2)) >= a__add(mark(X1),X2) ;
  mark(nil) >= nil ;
  mark(cons(X1,X2)) >= cons(X1,X2) ;
  mark(first(X1,X2)) >= a__first(mark(X1),mark(X2)) ;
  mark(from(X)) >= a__from(X) ;
  mark(and(X1,X2)) >= a__and(mark(X1),X2) ;
  mark(if(X1,X2,X3)) >= a__if(mark(X1),X2,X3) ;
  a__and(true,X) >= mark(X) ;
  a__and(false,Y) >= false ;
  a__and(X1,X2) >= and(X1,X2) ;
  a__if(true,X,Y) >= mark(X) ;
  a__if(false,X,Y) >= mark(Y) ;
  a__if(X1,X2,X3) >= if(X1,X2,X3) ;
  a__add(0,X) >= mark(X) ;
  a__add(s(X),Y) >= s(add(X,Y)) ;
  a__add(X1,X2) >= add(X1,X2) ;
  a__first(0,X) >= nil ;
  a__first(s(X),cons(Y,Z)) >= cons(Y,first(X,Z)) ;
  a__first(X1,X2) >= first(X1,X2) ;
  a__from(X) >= cons(X,from(s(X))) ;
  a__from(X) >= from(X) ;
  Marked_a__add(0,X) >= Marked_mark(X) ;
  Marked_a__if(true,X,Y) >= Marked_mark(X) ;
  Marked_a__if(false,X,Y) >= Marked_mark(Y) ;
  Marked_a__and(true,X) >= Marked_mark(X) ;
  Marked_mark(add(X1,X2)) >= Marked_a__add(mark(X1),X2) ;
  Marked_mark(add(X1,X2)) >= Marked_mark(X1) ;
  Marked_mark(first(X1,X2)) >= Marked_mark(X1) ;
  Marked_mark(first(X1,X2)) >= Marked_mark(X2) ;
  Marked_mark(and(X1,X2)) >= Marked_a__and(mark(X1),X2) ;
  Marked_mark(and(X1,X2)) >= Marked_mark(X1) ;
  Marked_mark(if(X1,X2,X3)) >= Marked_a__if(mark(X1),X2,X3) ;
  Marked_mark(if(X1,X2,X3)) >= Marked_mark(X1) ;
 }
 + Disjunctions:{ 
{
  Marked_a__add(0,X) > Marked_mark(X) ;
 }
{
  Marked_a__if(true,X,Y) > Marked_mark(X) ;
 }
{
  Marked_a__if(false,X,Y) > Marked_mark(Y) ;
 }
{
  Marked_a__and(true,X) > Marked_mark(X) ;
 }
{
  Marked_mark(add(X1,X2)) > Marked_a__add(mark(X1),X2) ;
 }
{
  Marked_mark(add(X1,X2)) > Marked_mark(X1) ;
 }
{
  Marked_mark(first(X1,X2)) > Marked_mark(X1) ;
 }
{
  Marked_mark(first(X1,X2)) > Marked_mark(X2) ;
 }
{
  Marked_mark(and(X1,X2)) > Marked_a__and(mark(X1),X2) ;
 }
{
  Marked_mark(and(X1,X2)) > Marked_mark(X1) ;
 }
{
  Marked_mark(if(X1,X2,X3)) > Marked_a__if(mark(X1),X2,X3) ;
 }
{
  Marked_mark(if(X1,X2,X3)) > Marked_mark(X1) ;
 }
 } 
=== 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: mark(true) >= true
constraint: mark(false) >= false
constraint: mark(0) >= 0
constraint: mark(s(X)) >= s(X)
constraint: mark(add(X1,X2)) >= a__add(mark(X1),X2)
constraint: mark(nil) >= nil
constraint: mark(cons(X1,X2)) >= cons(X1,X2)
constraint: mark(first(X1,X2)) >= a__first(mark(X1),mark(X2))
constraint: mark(from(X)) >= a__from(X)
constraint: mark(and(X1,X2)) >= a__and(mark(X1),X2)
constraint: mark(if(X1,X2,X3)) >= a__if(mark(X1),X2,X3)
constraint: a__and(true,X) >= mark(X)
constraint: a__and(false,Y) >= false
constraint: a__and(X1,X2) >= and(X1,X2)
constraint: a__if(true,X,Y) >= mark(X)
constraint: a__if(false,X,Y) >= mark(Y)
constraint: a__if(X1,X2,X3) >= if(X1,X2,X3)
constraint: a__add(0,X) >= mark(X)
constraint: a__add(s(X),Y) >= s(add(X,Y))
constraint: a__add(X1,X2) >= add(X1,X2)
constraint: a__first(0,X) >= nil
constraint: a__first(s(X),cons(Y,Z)) >= cons(Y,first(X,Z))
constraint: a__first(X1,X2) >= first(X1,X2)
constraint: a__from(X) >= cons(X,from(s(X)))
constraint: a__from(X) >= from(X)
constraint: Marked_a__add(0,X) >= Marked_mark(X)
constraint: Marked_a__if(true,X,Y) >= Marked_mark(X)
constraint: Marked_a__if(false,X,Y) >= Marked_mark(Y)
constraint: Marked_a__and(true,X) >= Marked_mark(X)
constraint: Marked_mark(add(X1,X2)) >= Marked_a__add(mark(X1),X2)
constraint: Marked_mark(add(X1,X2)) >= Marked_mark(X1)
constraint: Marked_mark(first(X1,X2)) >= Marked_mark(X1)
constraint: Marked_mark(first(X1,X2)) >= Marked_mark(X2)
constraint: Marked_mark(and(X1,X2)) >= Marked_a__and(mark(X1),X2)
constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1)
constraint: Marked_mark(if(X1,X2,X3)) >= Marked_a__if(mark(X1),X2,X3)
constraint: Marked_mark(if(X1,X2,X3)) >= Marked_mark(X1)
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_mark(first(X1,X2)) , Marked_mark(X2)> 
      --> <Marked_mark(first(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(first(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(first(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(first(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(add(X1,X2)) , Marked_a__add(mark(X1),X2)>
  <Marked_mark(first(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(first(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_a__if(mark(X1),X2,X3)>
  <Marked_mark(first(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(first(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
  <Marked_mark(first(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(first(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(first(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(first(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(add(X1,X2)) , Marked_a__add(mark(X1),X2)>
  <Marked_mark(first(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(first(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_a__if(mark(X1),X2,X3)>
  <Marked_mark(first(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(first(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
  <Marked_mark(add(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(add(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(add(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(add(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(add(X1,X2)) , Marked_a__add(mark(X1),X2)>
  <Marked_mark(add(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(add(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_a__if(mark(X1),X2,X3)>
  <Marked_mark(add(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(add(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
  <Marked_mark(add(X1,X2)) , Marked_a__add(mark(X1),X2)> 
     --> <Marked_a__add(0,X) , Marked_mark(X)>
  <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(add(X1,X2)) , Marked_a__add(mark(X1),X2)>
  <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_a__if(mark(X1),X2,X3)>
  <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
  <Marked_mark(if(X1,X2,X3)) , Marked_a__if(mark(X1),X2,X3)> 
     --> <Marked_a__if(false,X,Y) , Marked_mark(Y)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(add(X1,X2)) , Marked_a__add(mark(X1),X2)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_a__if(mark(X1),X2,X3)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
  <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)> 
     --> <Marked_a__and(true,X) , Marked_mark(X)>
  <Marked_a__add(0,X) , Marked_mark(X)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X2)>
  <Marked_a__add(0,X) , Marked_mark(X)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X1)>
  <Marked_a__add(0,X) , Marked_mark(X)> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X1)>
  <Marked_a__add(0,X) , Marked_mark(X)> 
     --> <Marked_mark(add(X1,X2)) , Marked_a__add(mark(X1),X2)>
  <Marked_a__add(0,X) , Marked_mark(X)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_a__add(0,X) , Marked_mark(X)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_a__if(mark(X1),X2,X3)>
  <Marked_a__add(0,X) , Marked_mark(X)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_a__add(0,X) , Marked_mark(X)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
  <Marked_a__if(false,X,Y) , Marked_mark(Y)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X2)>
  <Marked_a__if(false,X,Y) , Marked_mark(Y)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X1)>
  <Marked_a__if(false,X,Y) , Marked_mark(Y)> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X1)>
  <Marked_a__if(false,X,Y) , Marked_mark(Y)> 
     --> <Marked_mark(add(X1,X2)) , Marked_a__add(mark(X1),X2)>
  <Marked_a__if(false,X,Y) , Marked_mark(Y)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_a__if(false,X,Y) , Marked_mark(Y)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_a__if(mark(X1),X2,X3)>
  <Marked_a__if(false,X,Y) , Marked_mark(Y)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_a__if(false,X,Y) , Marked_mark(Y)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
  <Marked_a__and(true,X) , Marked_mark(X)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X2)>
  <Marked_a__and(true,X) , Marked_mark(X)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X1)>
  <Marked_a__and(true,X) , Marked_mark(X)> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X1)>
  <Marked_a__and(true,X) , Marked_mark(X)> 
     --> <Marked_mark(add(X1,X2)) , Marked_a__add(mark(X1),X2)>
  <Marked_a__and(true,X) , Marked_mark(X)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_a__and(true,X) , Marked_mark(X)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_a__if(mark(X1),X2,X3)>
  <Marked_a__and(true,X) , Marked_mark(X)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_a__and(true,X) , Marked_mark(X)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  mark(true) >= true ;
  mark(false) >= false ;
  mark(0) >= 0 ;
  mark(s(X)) >= s(X) ;
  mark(add(X1,X2)) >= a__add(mark(X1),X2) ;
  mark(nil) >= nil ;
  mark(cons(X1,X2)) >= cons(X1,X2) ;
  mark(first(X1,X2)) >= a__first(mark(X1),mark(X2)) ;
  mark(from(X)) >= a__from(X) ;
  mark(and(X1,X2)) >= a__and(mark(X1),X2) ;
  mark(if(X1,X2,X3)) >= a__if(mark(X1),X2,X3) ;
  a__and(true,X) >= mark(X) ;
  a__and(false,Y) >= false ;
  a__and(X1,X2) >= and(X1,X2) ;
  a__if(true,X,Y) >= mark(X) ;
  a__if(false,X,Y) >= mark(Y) ;
  a__if(X1,X2,X3) >= if(X1,X2,X3) ;
  a__add(0,X) >= mark(X) ;
  a__add(s(X),Y) >= s(add(X,Y)) ;
  a__add(X1,X2) >= add(X1,X2) ;
  a__first(0,X) >= nil ;
  a__first(s(X),cons(Y,Z)) >= cons(Y,first(X,Z)) ;
  a__first(X1,X2) >= first(X1,X2) ;
  a__from(X) >= cons(X,from(s(X))) ;
  a__from(X) >= from(X) ;
  Marked_a__add(0,X) >= Marked_mark(X) ;
  Marked_a__if(false,X,Y) >= Marked_mark(Y) ;
  Marked_a__and(true,X) >= Marked_mark(X) ;
  Marked_mark(add(X1,X2)) >= Marked_a__add(mark(X1),X2) ;
  Marked_mark(add(X1,X2)) >= Marked_mark(X1) ;
  Marked_mark(first(X1,X2)) >= Marked_mark(X1) ;
  Marked_mark(first(X1,X2)) >= Marked_mark(X2) ;
  Marked_mark(and(X1,X2)) >= Marked_a__and(mark(X1),X2) ;
  Marked_mark(and(X1,X2)) >= Marked_mark(X1) ;
  Marked_mark(if(X1,X2,X3)) >= Marked_a__if(mark(X1),X2,X3) ;
  Marked_mark(if(X1,X2,X3)) >= Marked_mark(X1) ;
 }
 + Disjunctions:{ 
{
  Marked_a__add(0,X) > Marked_mark(X) ;
 }
{
  Marked_a__if(false,X,Y) > Marked_mark(Y) ;
 }
{
  Marked_a__and(true,X) > Marked_mark(X) ;
 }
{
  Marked_mark(add(X1,X2)) > Marked_a__add(mark(X1),X2) ;
 }
{
  Marked_mark(add(X1,X2)) > Marked_mark(X1) ;
 }
{
  Marked_mark(first(X1,X2)) > Marked_mark(X1) ;
 }
{
  Marked_mark(first(X1,X2)) > Marked_mark(X2) ;
 }
{
  Marked_mark(and(X1,X2)) > Marked_a__and(mark(X1),X2) ;
 }
{
  Marked_mark(and(X1,X2)) > Marked_mark(X1) ;
 }
{
  Marked_mark(if(X1,X2,X3)) > Marked_a__if(mark(X1),X2,X3) ;
 }
{
  Marked_mark(if(X1,X2,X3)) > Marked_mark(X1) ;
 }
 } 
=== 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: mark(true) >= true
constraint: mark(false) >= false
constraint: mark(0) >= 0
constraint: mark(s(X)) >= s(X)
constraint: mark(add(X1,X2)) >= a__add(mark(X1),X2)
constraint: mark(nil) >= nil
constraint: mark(cons(X1,X2)) >= cons(X1,X2)
constraint: mark(first(X1,X2)) >= a__first(mark(X1),mark(X2))
constraint: mark(from(X)) >= a__from(X)
constraint: mark(and(X1,X2)) >= a__and(mark(X1),X2)
constraint: mark(if(X1,X2,X3)) >= a__if(mark(X1),X2,X3)
constraint: a__and(true,X) >= mark(X)
constraint: a__and(false,Y) >= false
constraint: a__and(X1,X2) >= and(X1,X2)
constraint: a__if(true,X,Y) >= mark(X)
constraint: a__if(false,X,Y) >= mark(Y)
constraint: a__if(X1,X2,X3) >= if(X1,X2,X3)
constraint: a__add(0,X) >= mark(X)
constraint: a__add(s(X),Y) >= s(add(X,Y))
constraint: a__add(X1,X2) >= add(X1,X2)
constraint: a__first(0,X) >= nil
constraint: a__first(s(X),cons(Y,Z)) >= cons(Y,first(X,Z))
constraint: a__first(X1,X2) >= first(X1,X2)
constraint: a__from(X) >= cons(X,from(s(X)))
constraint: a__from(X) >= from(X)
constraint: Marked_a__add(0,X) >= Marked_mark(X)
constraint: Marked_a__if(false,X,Y) >= Marked_mark(Y)
constraint: Marked_a__and(true,X) >= Marked_mark(X)
constraint: Marked_mark(add(X1,X2)) >= Marked_a__add(mark(X1),X2)
constraint: Marked_mark(add(X1,X2)) >= Marked_mark(X1)
constraint: Marked_mark(first(X1,X2)) >= Marked_mark(X1)
constraint: Marked_mark(first(X1,X2)) >= Marked_mark(X2)
constraint: Marked_mark(and(X1,X2)) >= Marked_a__and(mark(X1),X2)
constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1)
constraint: Marked_mark(if(X1,X2,X3)) >= Marked_a__if(mark(X1),X2,X3)
constraint: Marked_mark(if(X1,X2,X3)) >= Marked_mark(X1)
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_mark(add(X1,X2)) , Marked_mark(X1)> 
      --> <Marked_mark(add(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(add(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(add(X1,X2)) , Marked_a__add(mark(X1),X2)>
  <Marked_mark(add(X1,X2)) , Marked_a__add(mark(X1),X2)> 
     --> <Marked_a__add(0,X) , Marked_mark(X)>
  <Marked_a__add(0,X) , Marked_mark(X)> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X1)>
  <Marked_a__add(0,X) , Marked_mark(X)> 
     --> <Marked_mark(add(X1,X2)) , Marked_a__add(mark(X1),X2)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  mark(true) >= true ;
  mark(false) >= false ;
  mark(0) >= 0 ;
  mark(s(X)) >= s(X) ;
  mark(add(X1,X2)) >= a__add(mark(X1),X2) ;
  mark(nil) >= nil ;
  mark(cons(X1,X2)) >= cons(X1,X2) ;
  mark(first(X1,X2)) >= a__first(mark(X1),mark(X2)) ;
  mark(from(X)) >= a__from(X) ;
  mark(and(X1,X2)) >= a__and(mark(X1),X2) ;
  mark(if(X1,X2,X3)) >= a__if(mark(X1),X2,X3) ;
  a__and(true,X) >= mark(X) ;
  a__and(false,Y) >= false ;
  a__and(X1,X2) >= and(X1,X2) ;
  a__if(true,X,Y) >= mark(X) ;
  a__if(false,X,Y) >= mark(Y) ;
  a__if(X1,X2,X3) >= if(X1,X2,X3) ;
  a__add(0,X) >= mark(X) ;
  a__add(s(X),Y) >= s(add(X,Y)) ;
  a__add(X1,X2) >= add(X1,X2) ;
  a__first(0,X) >= nil ;
  a__first(s(X),cons(Y,Z)) >= cons(Y,first(X,Z)) ;
  a__first(X1,X2) >= first(X1,X2) ;
  a__from(X) >= cons(X,from(s(X))) ;
  a__from(X) >= from(X) ;
  Marked_a__add(0,X) >= Marked_mark(X) ;
  Marked_mark(add(X1,X2)) >= Marked_a__add(mark(X1),X2) ;
  Marked_mark(add(X1,X2)) >= Marked_mark(X1) ;
 }
 + Disjunctions:{ 
{
  Marked_a__add(0,X) > Marked_mark(X) ;
 }
{
  Marked_mark(add(X1,X2)) > Marked_a__add(mark(X1),X2) ;
 }
{
  Marked_mark(add(X1,X2)) > Marked_mark(X1) ;
 }
 } 
=== 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: mark(true) >= true
constraint: mark(false) >= false
constraint: mark(0) >= 0
constraint: mark(s(X)) >= s(X)
constraint: mark(add(X1,X2)) >= a__add(mark(X1),X2)
constraint: mark(nil) >= nil
constraint: mark(cons(X1,X2)) >= cons(X1,X2)
constraint: mark(first(X1,X2)) >= a__first(mark(X1),mark(X2))
constraint: mark(from(X)) >= a__from(X)
constraint: mark(and(X1,X2)) >= a__and(mark(X1),X2)
constraint: mark(if(X1,X2,X3)) >= a__if(mark(X1),X2,X3)
constraint: a__and(true,X) >= mark(X)
constraint: a__and(false,Y) >= false
constraint: a__and(X1,X2) >= and(X1,X2)
constraint: a__if(true,X,Y) >= mark(X)
constraint: a__if(false,X,Y) >= mark(Y)
constraint: a__if(X1,X2,X3) >= if(X1,X2,X3)
constraint: a__add(0,X) >= mark(X)
constraint: a__add(s(X),Y) >= s(add(X,Y))
constraint: a__add(X1,X2) >= add(X1,X2)
constraint: a__first(0,X) >= nil
constraint: a__first(s(X),cons(Y,Z)) >= cons(Y,first(X,Z))
constraint: a__first(X1,X2) >= first(X1,X2)
constraint: a__from(X) >= cons(X,from(s(X)))
constraint: a__from(X) >= from(X)
constraint: Marked_a__add(0,X) >= Marked_mark(X)
constraint: Marked_mark(add(X1,X2)) >= Marked_a__add(mark(X1),X2)
constraint: Marked_mark(add(X1,X2)) >= Marked_mark(X1)
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] a__and(true,X) -> mark(X)
[2] a__and(false,Y) -> false
[3] a__if(true,X,Y) -> mark(X)
[4] a__if(false,X,Y) -> mark(Y)
[5] a__add(0,X) -> mark(X)
[6] a__add(s(X),Y) -> s(add(X,Y))
[7] a__first(0,X) -> nil
[8] a__first(s(X),cons(Y,Z)) -> cons(Y,first(X,Z))
[9] a__from(X) -> cons(X,from(s(X)))
[10] mark(and(X1,X2)) -> a__and(mark(X1),X2)
[11] mark(if(X1,X2,X3)) -> a__if(mark(X1),X2,X3)
[12] mark(add(X1,X2)) -> a__add(mark(X1),X2)
[13] mark(first(X1,X2)) -> a__first(mark(X1),mark(X2))
[14] mark(from(X)) -> a__from(X)
[15] mark(true) -> true
[16] mark(false) -> false
[17] mark(0) -> 0
[18] mark(s(X)) -> s(X)
[19] mark(nil) -> nil
[20] mark(cons(X1,X2)) -> cons(X1,X2)
[21] a__and(X1,X2) -> and(X1,X2)
[22] a__if(X1,X2,X3) -> if(X1,X2,X3)
[23] a__add(X1,X2) -> add(X1,X2)
[24] a__first(X1,X2) -> first(X1,X2)
[25] a__from(X) -> from(X)
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_a__and(true,X) , Marked_mark(X)>
<Marked_a__if(true,X,Y) , Marked_mark(X)>
<Marked_a__if(false,X,Y) , Marked_mark(Y)>
<Marked_a__add(0,X) , Marked_mark(X)>
<Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
<Marked_mark(and(X1,X2)) , Marked_mark(X1)>
<Marked_mark(if(X1,X2,X3)) , Marked_a__if(mark(X1),X2,X3)>
<Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)>
<Marked_mark(add(X1,X2)) , Marked_a__add(mark(X1),X2)>
<Marked_mark(add(X1,X2)) , Marked_mark(X1)>
<Marked_mark(first(X1,X2)) , Marked_a__first(mark(X1),mark(X2))>
<Marked_mark(first(X1,X2)) , Marked_mark(X1)>
<Marked_mark(first(X1,X2)) , Marked_mark(X2)>
<Marked_mark(from(X)) , Marked_a__from(X)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_a__and(true,X) , Marked_mark(X)>
<Marked_a__if(true,X,Y) , Marked_mark(X)>
<Marked_a__if(false,X,Y) , Marked_mark(Y)>
<Marked_a__add(0,X) , Marked_mark(X)>
<Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
<Marked_mark(and(X1,X2)) , Marked_mark(X1)>
<Marked_mark(if(X1,X2,X3)) , Marked_a__if(mark(X1),X2,X3)>
<Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)>
<Marked_mark(add(X1,X2)) , Marked_a__add(mark(X1),X2)>
<Marked_mark(add(X1,X2)) , Marked_mark(X1)>
<Marked_mark(first(X1,X2)) , Marked_mark(X1)>
<Marked_mark(first(X1,X2)) , Marked_mark(X2)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ mark ] (X0) = 2*X0; 
 [ if ] (X0,X1,X2) = 3*X2 + 3*X1 + 2*X0; 
 [ add ] (X0,X1) = 2*X1 + 1*X0; 
 [ a__if ] (X0,X1,X2) = 3*X2 + 3*X1 + 2*X0; 
 [ Marked_a__if ] (X0,X1,X2) = 3*X2 + 3*X1 + 2*X0 + 1; 
 [ first ] (X0,X1) = 2*X1 + 2*X0; 
 [ true ] () = 1; 
 [ a__first ] (X0,X1) = 2*X1 + 2*X0; 
 [ 0 ] () = 0; 
 [ Marked_mark ] (X0) = 2*X0 + 1; 
 [ a__from ] (X0) = 0; 
 [ a__and ] (X0,X1) = 3*X1 + 2*X0; 
 [ nil ] () = 0; 
 [ a__add ] (X0,X1) = 3*X1 + 1*X0; 
 [ Marked_a__and ] (X0,X1) = 3*X1 + 1; 
 [ from ] (X0) = 0; 
 [ false ] () = 0; 
 [ Marked_a__add ] (X0,X1) = 3*X1 + 1; 
 [ cons ] (X0,X1) = 0; 
 [ s ] (X0) = 0; 
 [ and ] (X0,X1) = 3*X1 + 2*X0; 
 removing <Marked_a__if(true,X,Y),Marked_mark(X)>
 [ {
      
     DP termination of:
     <Marked_a__and(true,X) , Marked_mark(X)>
<Marked_a__if(false,X,Y) , Marked_mark(Y)>
<Marked_a__add(0,X) , Marked_mark(X)>
<Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
<Marked_mark(and(X1,X2)) , Marked_mark(X1)>
<Marked_mark(if(X1,X2,X3)) , Marked_a__if(mark(X1),X2,X3)>
<Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)>
<Marked_mark(add(X1,X2)) , Marked_a__add(mark(X1),X2)>
<Marked_mark(add(X1,X2)) , Marked_mark(X1)>
<Marked_mark(first(X1,X2)) , Marked_mark(X1)>
<Marked_mark(first(X1,X2)) , Marked_mark(X2)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_a__and(true,X) , Marked_mark(X)>
<Marked_a__if(false,X,Y) , Marked_mark(Y)>
<Marked_a__add(0,X) , Marked_mark(X)>
<Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
<Marked_mark(and(X1,X2)) , Marked_mark(X1)>
<Marked_mark(if(X1,X2,X3)) , Marked_a__if(mark(X1),X2,X3)>
<Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)>
<Marked_mark(add(X1,X2)) , Marked_a__add(mark(X1),X2)>
<Marked_mark(add(X1,X2)) , Marked_mark(X1)>
<Marked_mark(first(X1,X2)) , Marked_mark(X1)>
<Marked_mark(first(X1,X2)) , Marked_mark(X2)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ mark ] (X0) = 3*X0 + 2; 
 [ if ] (X0,X1,X2) = 2*X2 + 2*X1 + 3*X0 + 3; 
 [ add ] (X0,X1) = 2*X1 + 1*X0; 
 [ a__if ] (X0,X1,X2) = 3*X2 + 3*X1 + 3*X0 + 3; 
 [ Marked_a__if ] (X0,X1,X2) = 3*X2 + 1*X1 + 2*X0 + 2; 
 [ first ] (X0,X1) = 2*X1 + 2*X0 + 3; 
 [ true ] () = 0; 
 [ a__first ] (X0,X1) = 2*X1 + 2*X0 + 3; 
 [ 0 ] () = 3; 
 [ Marked_mark ] (X0) = 2*X0 + 2; 
 [ a__from ] (X0) = 0; 
 [ a__and ] (X0,X1) = 3*X1 + 2*X0 + 2; 
 [ nil ] () = 0; 
 [ a__add ] (X0,X1) = 3*X1 + 1*X0; 
 [ Marked_a__and ] (X0,X1) = 3*X1 + 3; 
 [ from ] (X0) = 0; 
 [ false ] () = 0; 
 [ Marked_a__add ] (X0,X1) = 3*X1 + 2; 
 [ cons ] (X0,X1) = 0; 
 [ s ] (X0) = 0; 
 [ and ] (X0,X1) = 2*X1 + 2*X0 + 2; 
 removing <Marked_a__and(true,X),Marked_mark(X)><Marked_mark(and(X1,X2)),
Marked_a__and(mark(X1),X2)><Marked_mark(and(X1,X2)),Marked_mark(X1)><
Marked_mark(if(X1,X2,X3)),Marked_a__if(mark(X1),X2,X3)><Marked_mark(if(
                                                                    X1,
                                                                    X2,
                                                                    X3)),
Marked_mark(X1)><Marked_mark(first(X1,X2)),Marked_mark(X1)><Marked_mark(
                                                             first(X1,
                                                              X2)),Marked_mark(
                                                                    X2)>
 [ {
      
     DP termination of:
     <Marked_a__if(false,X,Y) , Marked_mark(Y)>
<Marked_a__add(0,X) , Marked_mark(X)>
<Marked_mark(add(X1,X2)) , Marked_a__add(mark(X1),X2)>
<Marked_mark(add(X1,X2)) , Marked_mark(X1)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_a__add(0,X) , Marked_mark(X)>
<Marked_mark(add(X1,X2)) , Marked_a__add(mark(X1),X2)>
<Marked_mark(add(X1,X2)) , Marked_mark(X1)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ mark ] (X0) = 2*X0 + 0; 
 [ if ] (X0,X1,X2) = 3*X1 + 3*X2 + 0; 
 [ add ] (X0,X1) = 1 + 1*X0 + 1*X1 + 0; 
 [ a__if ] (X0,X1,X2) = 3*X1 + 3*X2 + 0; 
 [ first ] (X0,X1) = 2 + 2*X0 + 0; 
 [ true ] () = 0; 
 [ a__first ] (X0,X1) = 2 + 2*X0 + 0; 
 [ 0 ] () = 1 + 0; 
 [ Marked_mark ] (X0) = 2 + 2*X0 + 0; 
 [ a__from ] (X0) = 0; 
 [ a__and ] (X0,X1) = 3*X1 + 0; 
 [ nil ] () = 0; 
 [ a__add ] (X0,X1) = 2 + 1*X0 + 2*X1 + 0; 
 [ from ] (X0) = 0; 
 [ false ] () = 0; 
 [ Marked_a__add ] (X0,X1) = 3 + 1*X0 + 2*X1 + 0; 
 [ cons ] (X0,X1) = 2*X1 + 0; 
 [ s ] (X0) = 3 + 2*X0 + 0; 
 [ and ] (X0,X1) = 3*X1 + 0; 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 

Cime worked for 0.323628 seconds (real time)
Cime Exit Status: 0