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

TRS termination of:
[1] from(X) -> cons(X,n__from(n__s(X)))
[2] first(0,Z) -> nil
[3] first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z)))
[4] sel(0,cons(X,Z)) -> X
[5] sel(s(X),cons(Y,Z)) -> sel(X,activate(Z))
[6] from(X) -> n__from(X)
[7] s(X) -> n__s(X)
[8] first(X1,X2) -> n__first(X1,X2)
[9] activate(n__from(X)) -> from(activate(X))
[10] activate(n__s(X)) -> s(activate(X))
[11] activate(n__first(X1,X2)) -> first(activate(X1),activate(X2))
[12] activate(X) -> X


Sub problem: 
guided: 

DP termination of:
<Marked_first(s(X),cons(Y,Z)) , Marked_activate(Z)>
<Marked_sel(s(X),cons(Y,Z)) , Marked_sel(X,activate(Z))>
<Marked_sel(s(X),cons(Y,Z)) , Marked_activate(Z)>
<Marked_activate(n__from(X)) , Marked_from(activate(X))>
<Marked_activate(n__from(X)) , Marked_activate(X)>
<Marked_activate(n__s(X)) , Marked_s(activate(X))>
<Marked_activate(n__s(X)) , Marked_activate(X)>
<Marked_activate(n__first(X1,X2)) , Marked_first(activate(X1),activate(X2))>
<Marked_activate(n__first(X1,X2)) , Marked_activate(X1)>
<Marked_activate(n__first(X1,X2)) , Marked_activate(X2)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <Marked_sel(s(X),cons(Y,Z)) , Marked_sel(X,activate(Z))> 
      --> <Marked_sel(s(X),cons(Y,Z)) , Marked_sel(X,activate(Z))>
}

{  <Marked_activate(n__first(X1,X2)) , Marked_activate(X2)> 
      --> <Marked_activate(n__first(X1,X2)) , Marked_activate(X2)>
  <Marked_activate(n__first(X1,X2)) , Marked_activate(X2)> 
     --> <Marked_activate(n__first(X1,X2)) , Marked_activate(X1)>
  <Marked_activate(n__first(X1,X2)) , Marked_activate(X2)> 
     --> <Marked_activate(n__first(X1,X2)) , Marked_first(activate(X1),
                                              activate(X2))>
  <Marked_activate(n__first(X1,X2)) , Marked_activate(X2)> 
     --> <Marked_activate(n__s(X)) , Marked_activate(X)>
  <Marked_activate(n__first(X1,X2)) , Marked_activate(X2)> 
     --> <Marked_activate(n__from(X)) , Marked_activate(X)>
  <Marked_activate(n__first(X1,X2)) , Marked_activate(X1)> 
     --> <Marked_activate(n__first(X1,X2)) , Marked_activate(X2)>
  <Marked_activate(n__first(X1,X2)) , Marked_activate(X1)> 
     --> <Marked_activate(n__first(X1,X2)) , Marked_activate(X1)>
  <Marked_activate(n__first(X1,X2)) , Marked_activate(X1)> 
     --> <Marked_activate(n__first(X1,X2)) , Marked_first(activate(X1),
                                              activate(X2))>
  <Marked_activate(n__first(X1,X2)) , Marked_activate(X1)> 
     --> <Marked_activate(n__s(X)) , Marked_activate(X)>
  <Marked_activate(n__first(X1,X2)) , Marked_activate(X1)> 
     --> <Marked_activate(n__from(X)) , Marked_activate(X)>
  <Marked_activate(n__first(X1,X2)) , Marked_first(activate(X1),activate(X2))> 
     --> <Marked_first(s(X),cons(Y,Z)) , Marked_activate(Z)>
  <Marked_activate(n__s(X)) , Marked_activate(X)> 
     --> <Marked_activate(n__first(X1,X2)) , Marked_activate(X2)>
  <Marked_activate(n__s(X)) , Marked_activate(X)> 
     --> <Marked_activate(n__first(X1,X2)) , Marked_activate(X1)>
  <Marked_activate(n__s(X)) , Marked_activate(X)> 
     --> <Marked_activate(n__first(X1,X2)) , Marked_first(activate(X1),
                                              activate(X2))>
  <Marked_activate(n__s(X)) , Marked_activate(X)> 
     --> <Marked_activate(n__s(X)) , Marked_activate(X)>
  <Marked_activate(n__s(X)) , Marked_activate(X)> 
     --> <Marked_activate(n__from(X)) , Marked_activate(X)>
  <Marked_activate(n__from(X)) , Marked_activate(X)> 
     --> <Marked_activate(n__first(X1,X2)) , Marked_activate(X2)>
  <Marked_activate(n__from(X)) , Marked_activate(X)> 
     --> <Marked_activate(n__first(X1,X2)) , Marked_activate(X1)>
  <Marked_activate(n__from(X)) , Marked_activate(X)> 
     --> <Marked_activate(n__first(X1,X2)) , Marked_first(activate(X1),
                                              activate(X2))>
  <Marked_activate(n__from(X)) , Marked_activate(X)> 
     --> <Marked_activate(n__s(X)) , Marked_activate(X)>
  <Marked_activate(n__from(X)) , Marked_activate(X)> 
     --> <Marked_activate(n__from(X)) , Marked_activate(X)>
  <Marked_first(s(X),cons(Y,Z)) , Marked_activate(Z)> 
     --> <Marked_activate(n__first(X1,X2)) , Marked_activate(X2)>
  <Marked_first(s(X),cons(Y,Z)) , Marked_activate(Z)> 
     --> <Marked_activate(n__first(X1,X2)) , Marked_activate(X1)>
  <Marked_first(s(X),cons(Y,Z)) , Marked_activate(Z)> 
     --> <Marked_activate(n__first(X1,X2)) , Marked_first(activate(X1),
                                              activate(X2))>
  <Marked_first(s(X),cons(Y,Z)) , Marked_activate(Z)> 
     --> <Marked_activate(n__s(X)) , Marked_activate(X)>
  <Marked_first(s(X),cons(Y,Z)) , Marked_activate(Z)> 
     --> <Marked_activate(n__from(X)) , Marked_activate(X)>
}
APPLY CRITERIA (Subterm criterion)

ST: Marked_sel -> 1

APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  from(X) >= cons(X,n__from(n__s(X))) ;
  from(X) >= n__from(X) ;
  first(0,Z) >= nil ;
  first(s(X),cons(Y,Z)) >= cons(Y,n__first(X,activate(Z))) ;
  first(X1,X2) >= n__first(X1,X2) ;
  activate(n__from(X)) >= from(activate(X)) ;
  activate(n__s(X)) >= s(activate(X)) ;
  activate(n__first(X1,X2)) >= first(activate(X1),activate(X2)) ;
  activate(X) >= X ;
  s(X) >= n__s(X) ;
  sel(0,cons(X,Z)) >= X ;
  sel(s(X),cons(Y,Z)) >= sel(X,activate(Z)) ;
  Marked_activate(n__from(X)) >= Marked_activate(X) ;
  Marked_activate(n__s(X)) >= Marked_activate(X) ;
  Marked_activate(n__first(X1,X2)) >= Marked_activate(X1) ;
  Marked_activate(n__first(X1,X2)) >= Marked_activate(X2) ;
  Marked_activate(n__first(X1,X2)) >= Marked_first(activate(X1),activate(X2)) ;
  Marked_first(s(X),cons(Y,Z)) >= Marked_activate(Z) ;
 }
 + Disjunctions:{ 
{
  Marked_activate(n__from(X)) > Marked_activate(X) ;
 }
{
  Marked_activate(n__s(X)) > Marked_activate(X) ;
 }
{
  Marked_activate(n__first(X1,X2)) > Marked_activate(X1) ;
 }
{
  Marked_activate(n__first(X1,X2)) > Marked_activate(X2) ;
 }
{
  Marked_activate(n__first(X1,X2)) > Marked_first(activate(X1),activate(X2)) ;
 }
{
  Marked_first(s(X),cons(Y,Z)) > Marked_activate(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 : 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 (Simple graph)
Found the following constraints:
{
  from(X) >= cons(X,n__from(n__s(X))) ;
  from(X) >= n__from(X) ;
  first(0,Z) >= nil ;
  first(s(X),cons(Y,Z)) >= cons(Y,n__first(X,activate(Z))) ;
  first(X1,X2) >= n__first(X1,X2) ;
  activate(n__from(X)) >= from(activate(X)) ;
  activate(n__s(X)) >= s(activate(X)) ;
  activate(n__first(X1,X2)) >= first(activate(X1),activate(X2)) ;
  activate(X) >= X ;
  s(X) >= n__s(X) ;
  sel(0,cons(X,Z)) >= X ;
  sel(s(X),cons(Y,Z)) >= sel(X,activate(Z)) ;
  Marked_activate(n__from(X)) > Marked_activate(X) ;
  Marked_activate(n__s(X)) > Marked_activate(X) ;
  Marked_activate(n__first(X1,X2)) > Marked_activate(X1) ;
  Marked_activate(n__first(X1,X2)) > Marked_activate(X2) ;
  Marked_activate(n__first(X1,X2)) >= Marked_first(activate(X1),activate(X2)) ;
  Marked_first(s(X),cons(Y,Z)) > Marked_activate(Z) ;
 }

APPLY CRITERIA (SOLVE_ORD)
Trying to solve the following constraints:
{
  from(X) >= cons(X,n__from(n__s(X))) ;
  from(X) >= n__from(X) ;
  first(0,Z) >= nil ;
  first(s(X),cons(Y,Z)) >= cons(Y,n__first(X,activate(Z))) ;
  first(X1,X2) >= n__first(X1,X2) ;
  activate(n__from(X)) >= from(activate(X)) ;
  activate(n__s(X)) >= s(activate(X)) ;
  activate(n__first(X1,X2)) >= first(activate(X1),activate(X2)) ;
  activate(X) >= X ;
  s(X) >= n__s(X) ;
  sel(0,cons(X,Z)) >= X ;
  sel(s(X),cons(Y,Z)) >= sel(X,activate(Z)) ;
  Marked_activate(n__from(X)) > Marked_activate(X) ;
  Marked_activate(n__s(X)) > Marked_activate(X) ;
  Marked_activate(n__first(X1,X2)) > Marked_activate(X1) ;
  Marked_activate(n__first(X1,X2)) > Marked_activate(X2) ;
  Marked_activate(n__first(X1,X2)) >= Marked_first(activate(X1),activate(X2)) ;
  Marked_first(s(X),cons(Y,Z)) > Marked_activate(Z) ;
 }
 + Disjunctions:{ 
 } 
=== 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 ===
No solution found for these parameters.(411 bt (400) [167])
=== 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 3.205195 seconds (real time)
Cime Exit Status: 0