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

TRS termination of:
[1] terms(N) -> cons(recip(sqr(N)),n__terms(s(N)))
[2] sqr(0) -> 0
[3] sqr(s(X)) -> s(n__add(sqr(activate(X)),dbl(activate(X))))
[4] dbl(0) -> 0
[5] dbl(s(X)) -> s(n__s(n__dbl(activate(X))))
[6] add(0,X) -> X
[7] add(s(X),Y) -> s(n__add(activate(X),Y))
[8] first(0,X) -> nil
[9] first(s(X),cons(Y,Z)) -> cons(Y,n__first(activate(X),activate(Z)))
[10] terms(X) -> n__terms(X)
[11] add(X1,X2) -> n__add(X1,X2)
[12] s(X) -> n__s(X)
[13] dbl(X) -> n__dbl(X)
[14] first(X1,X2) -> n__first(X1,X2)
[15] activate(n__terms(X)) -> terms(X)
[16] activate(n__add(X1,X2)) -> add(X1,X2)
[17] activate(n__s(X)) -> s(X)
[18] activate(n__dbl(X)) -> dbl(X)
[19] activate(n__first(X1,X2)) -> first(X1,X2)
[20] activate(X) -> X


Sub problem: 
guided: 

DP termination of:
<Marked_terms(N) , Marked_sqr(N)>
<Marked_terms(N) , Marked_s(N)>
<Marked_sqr(s(X)) , Marked_s(n__add(sqr(activate(X)),dbl(activate(X))))>
<Marked_sqr(s(X)) , Marked_sqr(activate(X))>
<Marked_sqr(s(X)) , Marked_activate(X)>
<Marked_sqr(s(X)) , Marked_dbl(activate(X))>
<Marked_sqr(s(X)) , Marked_activate(X)>
<Marked_dbl(s(X)) , Marked_s(n__s(n__dbl(activate(X))))>
<Marked_dbl(s(X)) , Marked_activate(X)>
<Marked_add(s(X),Y) , Marked_s(n__add(activate(X),Y))>
<Marked_add(s(X),Y) , Marked_activate(X)>
<Marked_first(s(X),cons(Y,Z)) , Marked_activate(X)>
<Marked_first(s(X),cons(Y,Z)) , Marked_activate(Z)>
<Marked_activate(n__terms(X)) , Marked_terms(X)>
<Marked_activate(n__add(X1,X2)) , Marked_add(X1,X2)>
<Marked_activate(n__s(X)) , Marked_s(X)>
<Marked_activate(n__dbl(X)) , Marked_dbl(X)>
<Marked_activate(n__first(X1,X2)) , Marked_first(X1,X2)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_activate(n__first(X1,X2)) , Marked_first(X1,X2)> 
      --> <Marked_first(s(X),cons(Y,Z)) , Marked_activate(Z)>
  <Marked_activate(n__first(X1,X2)) , Marked_first(X1,X2)> 
     --> <Marked_first(s(X),cons(Y,Z)) , Marked_activate(X)>
  <Marked_activate(n__dbl(X)) , Marked_dbl(X)> 
     --> <Marked_dbl(s(X)) , Marked_activate(X)>
  <Marked_activate(n__add(X1,X2)) , Marked_add(X1,X2)> 
     --> <Marked_add(s(X),Y) , Marked_activate(X)>
  <Marked_activate(n__terms(X)) , Marked_terms(X)> 
     --> <Marked_terms(N) , Marked_sqr(N)>
  <Marked_first(s(X),cons(Y,Z)) , Marked_activate(Z)> 
     --> <Marked_activate(n__first(X1,X2)) , Marked_first(X1,X2)>
  <Marked_first(s(X),cons(Y,Z)) , Marked_activate(Z)> 
     --> <Marked_activate(n__dbl(X)) , Marked_dbl(X)>
  <Marked_first(s(X),cons(Y,Z)) , Marked_activate(Z)> 
     --> <Marked_activate(n__add(X1,X2)) , Marked_add(X1,X2)>
  <Marked_first(s(X),cons(Y,Z)) , Marked_activate(Z)> 
     --> <Marked_activate(n__terms(X)) , Marked_terms(X)>
  <Marked_first(s(X),cons(Y,Z)) , Marked_activate(X)> 
     --> <Marked_activate(n__first(X1,X2)) , Marked_first(X1,X2)>
  <Marked_first(s(X),cons(Y,Z)) , Marked_activate(X)> 
     --> <Marked_activate(n__dbl(X)) , Marked_dbl(X)>
  <Marked_first(s(X),cons(Y,Z)) , Marked_activate(X)> 
     --> <Marked_activate(n__add(X1,X2)) , Marked_add(X1,X2)>
  <Marked_first(s(X),cons(Y,Z)) , Marked_activate(X)> 
     --> <Marked_activate(n__terms(X)) , Marked_terms(X)>
  <Marked_add(s(X),Y) , Marked_activate(X)> 
     --> <Marked_activate(n__first(X1,X2)) , Marked_first(X1,X2)>
  <Marked_add(s(X),Y) , Marked_activate(X)> 
     --> <Marked_activate(n__dbl(X)) , Marked_dbl(X)>
  <Marked_add(s(X),Y) , Marked_activate(X)> 
     --> <Marked_activate(n__add(X1,X2)) , Marked_add(X1,X2)>
  <Marked_add(s(X),Y) , Marked_activate(X)> 
     --> <Marked_activate(n__terms(X)) , Marked_terms(X)>
  <Marked_dbl(s(X)) , Marked_activate(X)> 
     --> <Marked_activate(n__first(X1,X2)) , Marked_first(X1,X2)>
  <Marked_dbl(s(X)) , Marked_activate(X)> 
     --> <Marked_activate(n__dbl(X)) , Marked_dbl(X)>
  <Marked_dbl(s(X)) , Marked_activate(X)> 
     --> <Marked_activate(n__add(X1,X2)) , Marked_add(X1,X2)>
  <Marked_dbl(s(X)) , Marked_activate(X)> 
     --> <Marked_activate(n__terms(X)) , Marked_terms(X)>
  <Marked_sqr(s(X)) , Marked_activate(X)> 
     --> <Marked_activate(n__first(X1,X2)) , Marked_first(X1,X2)>
  <Marked_sqr(s(X)) , Marked_activate(X)> 
     --> <Marked_activate(n__dbl(X)) , Marked_dbl(X)>
  <Marked_sqr(s(X)) , Marked_activate(X)> 
     --> <Marked_activate(n__add(X1,X2)) , Marked_add(X1,X2)>
  <Marked_sqr(s(X)) , Marked_activate(X)> 
     --> <Marked_activate(n__terms(X)) , Marked_terms(X)>
  <Marked_sqr(s(X)) , Marked_dbl(activate(X))> 
     --> <Marked_dbl(s(X)) , Marked_activate(X)>
  <Marked_sqr(s(X)) , Marked_activate(X)> 
     --> <Marked_activate(n__first(X1,X2)) , Marked_first(X1,X2)>
  <Marked_sqr(s(X)) , Marked_activate(X)> 
     --> <Marked_activate(n__dbl(X)) , Marked_dbl(X)>
  <Marked_sqr(s(X)) , Marked_activate(X)> 
     --> <Marked_activate(n__add(X1,X2)) , Marked_add(X1,X2)>
  <Marked_sqr(s(X)) , Marked_activate(X)> 
     --> <Marked_activate(n__terms(X)) , Marked_terms(X)>
  <Marked_sqr(s(X)) , Marked_sqr(activate(X))> 
     --> <Marked_sqr(s(X)) , Marked_activate(X)>
  <Marked_sqr(s(X)) , Marked_sqr(activate(X))> 
     --> <Marked_sqr(s(X)) , Marked_dbl(activate(X))>
  <Marked_sqr(s(X)) , Marked_sqr(activate(X))> 
     --> <Marked_sqr(s(X)) , Marked_activate(X)>
  <Marked_sqr(s(X)) , Marked_sqr(activate(X))> 
     --> <Marked_sqr(s(X)) , Marked_sqr(activate(X))>
  <Marked_terms(N) , Marked_sqr(N)> --> <Marked_sqr(s(X)) , Marked_activate(X)>
  <Marked_terms(N) , Marked_sqr(N)> 
     --> <Marked_sqr(s(X)) , Marked_dbl(activate(X))>
  <Marked_terms(N) , Marked_sqr(N)> --> <Marked_sqr(s(X)) , Marked_activate(X)>
  <Marked_terms(N) , Marked_sqr(N)> 
     --> <Marked_sqr(s(X)) , Marked_sqr(activate(X))>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  sqr(s(X)) >= s(n__add(sqr(activate(X)),dbl(activate(X)))) ;
  sqr(0) >= 0 ;
  s(X) >= n__s(X) ;
  terms(N) >= cons(recip(sqr(N)),n__terms(s(N))) ;
  terms(X) >= n__terms(X) ;
  activate(n__terms(X)) >= terms(X) ;
  activate(n__add(X1,X2)) >= add(X1,X2) ;
  activate(n__s(X)) >= s(X) ;
  activate(n__dbl(X)) >= dbl(X) ;
  activate(n__first(X1,X2)) >= first(X1,X2) ;
  activate(X) >= X ;
  dbl(s(X)) >= s(n__s(n__dbl(activate(X)))) ;
  dbl(0) >= 0 ;
  dbl(X) >= n__dbl(X) ;
  add(s(X),Y) >= s(n__add(activate(X),Y)) ;
  add(0,X) >= X ;
  add(X1,X2) >= n__add(X1,X2) ;
  first(s(X),cons(Y,Z)) >= cons(Y,n__first(activate(X),activate(Z))) ;
  first(0,X) >= nil ;
  first(X1,X2) >= n__first(X1,X2) ;
  Marked_activate(n__terms(X)) >= Marked_terms(X) ;
  Marked_activate(n__add(X1,X2)) >= Marked_add(X1,X2) ;
  Marked_activate(n__dbl(X)) >= Marked_dbl(X) ;
  Marked_activate(n__first(X1,X2)) >= Marked_first(X1,X2) ;
  Marked_first(s(X),cons(Y,Z)) >= Marked_activate(X) ;
  Marked_first(s(X),cons(Y,Z)) >= Marked_activate(Z) ;
  Marked_dbl(s(X)) >= Marked_activate(X) ;
  Marked_add(s(X),Y) >= Marked_activate(X) ;
  Marked_terms(N) >= Marked_sqr(N) ;
  Marked_sqr(s(X)) >= Marked_activate(X) ;
  Marked_sqr(s(X)) >= Marked_dbl(activate(X)) ;
  Marked_sqr(s(X)) >= Marked_sqr(activate(X)) ;
 }
 + Disjunctions:{ 
{
  Marked_activate(n__terms(X)) > Marked_terms(X) ;
 }
{
  Marked_activate(n__add(X1,X2)) > Marked_add(X1,X2) ;
 }
{
  Marked_activate(n__dbl(X)) > Marked_dbl(X) ;
 }
{
  Marked_activate(n__first(X1,X2)) > Marked_first(X1,X2) ;
 }
{
  Marked_first(s(X),cons(Y,Z)) > Marked_activate(X) ;
 }
{
  Marked_first(s(X),cons(Y,Z)) > Marked_activate(Z) ;
 }
{
  Marked_dbl(s(X)) > Marked_activate(X) ;
 }
{
  Marked_add(s(X),Y) > Marked_activate(X) ;
 }
{
  Marked_terms(N) > Marked_sqr(N) ;
 }
{
  Marked_sqr(s(X)) > Marked_activate(X) ;
 }
{
  Marked_sqr(s(X)) > Marked_dbl(activate(X)) ;
 }
{
  Marked_sqr(s(X)) > Marked_sqr(activate(X)) ;
 }
 } 
=== 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 ===
Time out for these parameters.
=== 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 timeout reached
=== 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 76.765843 seconds (real time)
Cime Exit Status: 0