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

TRS termination of:
[1] sel(s(X),cons(Y,Z)) -> sel(X,activate(Z))
[2] sel(0,cons(X,Z)) -> X
[3] first(0,Z) -> nil
[4] first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z)))
[5] from(X) -> cons(X,n__from(s(X)))
[6] sel1(s(X),cons(Y,Z)) -> sel1(X,activate(Z))
[7] sel1(0,cons(X,Z)) -> quote(X)
[8] first1(0,Z) -> nil1
[9] first1(s(X),cons(Y,Z)) -> cons1(quote(Y),first1(X,activate(Z)))
[10] quote(n__0) -> 01
[11] quote1(n__cons(X,Z)) -> cons1(quote(activate(X)),quote1(activate(Z)))
[12] quote1(n__nil) -> nil1
[13] quote(n__s(X)) -> s1(quote(activate(X)))
[14] quote(n__sel(X,Z)) -> sel1(activate(X),activate(Z))
[15] quote1(n__first(X,Z)) -> first1(activate(X),activate(Z))
[16] unquote(01) -> 0
[17] unquote(s1(X)) -> s(unquote(X))
[18] unquote1(nil1) -> nil
[19] unquote1(cons1(X,Z)) -> fcons(unquote(X),unquote1(Z))
[20] fcons(X,Z) -> cons(X,Z)
[21] first(X1,X2) -> n__first(X1,X2)
[22] from(X) -> n__from(X)
[23] 0 -> n__0
[24] cons(X1,X2) -> n__cons(X1,X2)
[25] nil -> n__nil
[26] s(X) -> n__s(X)
[27] sel(X1,X2) -> n__sel(X1,X2)
[28] activate(n__first(X1,X2)) -> first(X1,X2)
[29] activate(n__from(X)) -> from(X)
[30] activate(n__0) -> 0
[31] activate(n__cons(X1,X2)) -> cons(X1,X2)
[32] activate(n__nil) -> nil
[33] activate(n__s(X)) -> s(X)
[34] activate(n__sel(X1,X2)) -> sel(X1,X2)
[35] activate(X) -> X


Sub problem: 
guided: 

DP termination of:
<Marked_sel(s(X),cons(Y,Z)) , Marked_sel(X,activate(Z))>
<Marked_sel(s(X),cons(Y,Z)) , Marked_activate(Z)>
<Marked_first(0,Z) , Marked_nil>
<Marked_first(s(X),cons(Y,Z)) , Marked_cons(Y,n__first(X,activate(Z)))>
<Marked_first(s(X),cons(Y,Z)) , Marked_activate(Z)>
<Marked_from(X) , Marked_cons(X,n__from(s(X)))>
<Marked_from(X) , Marked_s(X)>
<Marked_sel1(s(X),cons(Y,Z)) , Marked_sel1(X,activate(Z))>
<Marked_sel1(s(X),cons(Y,Z)) , Marked_activate(Z)>
<Marked_sel1(0,cons(X,Z)) , Marked_quote(X)>
<Marked_first1(s(X),cons(Y,Z)) , Marked_quote(Y)>
<Marked_first1(s(X),cons(Y,Z)) , Marked_first1(X,activate(Z))>
<Marked_first1(s(X),cons(Y,Z)) , Marked_activate(Z)>
<Marked_quote1(n__cons(X,Z)) , Marked_quote(activate(X))>
<Marked_quote1(n__cons(X,Z)) , Marked_activate(X)>
<Marked_quote1(n__cons(X,Z)) , Marked_quote1(activate(Z))>
<Marked_quote1(n__cons(X,Z)) , Marked_activate(Z)>
<Marked_quote(n__s(X)) , Marked_quote(activate(X))>
<Marked_quote(n__s(X)) , Marked_activate(X)>
<Marked_quote(n__sel(X,Z)) , Marked_sel1(activate(X),activate(Z))>
<Marked_quote(n__sel(X,Z)) , Marked_activate(X)>
<Marked_quote(n__sel(X,Z)) , Marked_activate(Z)>
<Marked_quote1(n__first(X,Z)) , Marked_first1(activate(X),activate(Z))>
<Marked_quote1(n__first(X,Z)) , Marked_activate(X)>
<Marked_quote1(n__first(X,Z)) , Marked_activate(Z)>
<Marked_unquote(01) , Marked_0>
<Marked_unquote(s1(X)) , Marked_s(unquote(X))>
<Marked_unquote(s1(X)) , Marked_unquote(X)>
<Marked_unquote1(nil1) , Marked_nil>
<Marked_unquote1(cons1(X,Z)) , Marked_fcons(unquote(X),unquote1(Z))>
<Marked_unquote1(cons1(X,Z)) , Marked_unquote(X)>
<Marked_unquote1(cons1(X,Z)) , Marked_unquote1(Z)>
<Marked_fcons(X,Z) , Marked_cons(X,Z)>
<Marked_activate(n__first(X1,X2)) , Marked_first(X1,X2)>
<Marked_activate(n__from(X)) , Marked_from(X)>
<Marked_activate(n__0) , Marked_0>
<Marked_activate(n__cons(X1,X2)) , Marked_cons(X1,X2)>
<Marked_activate(n__nil) , Marked_nil>
<Marked_activate(n__s(X)) , Marked_s(X)>
<Marked_activate(n__sel(X1,X2)) , Marked_sel(X1,X2)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 6 components:

{  <Marked_quote1(n__cons(X,Z)) , Marked_quote1(activate(Z))> 
      --> <Marked_quote1(n__cons(X,Z)) , Marked_quote1(activate(Z))>
}

{  <Marked_first1(s(X),cons(Y,Z)) , Marked_first1(X,activate(Z))> 
      --> <Marked_first1(s(X),cons(Y,Z)) , Marked_first1(X,activate(Z))>
}

{  <Marked_quote(n__sel(X,Z)) , Marked_sel1(activate(X),activate(Z))> 
      --> <Marked_sel1(0,cons(X,Z)) , Marked_quote(X)>
  <Marked_quote(n__sel(X,Z)) , Marked_sel1(activate(X),activate(Z))> 
     --> <Marked_sel1(s(X),cons(Y,Z)) , Marked_sel1(X,activate(Z))>
  <Marked_quote(n__s(X)) , Marked_quote(activate(X))> 
     --> <Marked_quote(n__sel(X,Z)) , Marked_sel1(activate(X),activate(Z))>
  <Marked_quote(n__s(X)) , Marked_quote(activate(X))> 
     --> <Marked_quote(n__s(X)) , Marked_quote(activate(X))>
  <Marked_sel1(0,cons(X,Z)) , Marked_quote(X)> 
     --> <Marked_quote(n__sel(X,Z)) , Marked_sel1(activate(X),activate(Z))>
  <Marked_sel1(0,cons(X,Z)) , Marked_quote(X)> 
     --> <Marked_quote(n__s(X)) , Marked_quote(activate(X))>
  <Marked_sel1(s(X),cons(Y,Z)) , Marked_sel1(X,activate(Z))> 
     --> <Marked_sel1(0,cons(X,Z)) , Marked_quote(X)>
  <Marked_sel1(s(X),cons(Y,Z)) , Marked_sel1(X,activate(Z))> 
     --> <Marked_sel1(s(X),cons(Y,Z)) , Marked_sel1(X,activate(Z))>
}

{  <Marked_unquote1(cons1(X,Z)) , Marked_unquote1(Z)> 
      --> <Marked_unquote1(cons1(X,Z)) , Marked_unquote1(Z)>
}

{  <Marked_unquote(s1(X)) , Marked_unquote(X)> 
      --> <Marked_unquote(s1(X)) , Marked_unquote(X)>
}

{  <Marked_activate(n__sel(X1,X2)) , Marked_sel(X1,X2)> 
      --> <Marked_sel(s(X),cons(Y,Z)) , Marked_activate(Z)>
  <Marked_activate(n__sel(X1,X2)) , Marked_sel(X1,X2)> 
     --> <Marked_sel(s(X),cons(Y,Z)) , Marked_sel(X,activate(Z))>
  <Marked_activate(n__first(X1,X2)) , Marked_first(X1,X2)> 
     --> <Marked_first(s(X),cons(Y,Z)) , Marked_activate(Z)>
  <Marked_first(s(X),cons(Y,Z)) , Marked_activate(Z)> 
     --> <Marked_activate(n__sel(X1,X2)) , Marked_sel(X1,X2)>
  <Marked_first(s(X),cons(Y,Z)) , Marked_activate(Z)> 
     --> <Marked_activate(n__first(X1,X2)) , Marked_first(X1,X2)>
  <Marked_sel(s(X),cons(Y,Z)) , Marked_activate(Z)> 
     --> <Marked_activate(n__sel(X1,X2)) , Marked_sel(X1,X2)>
  <Marked_sel(s(X),cons(Y,Z)) , Marked_activate(Z)> 
     --> <Marked_activate(n__first(X1,X2)) , Marked_first(X1,X2)>
  <Marked_sel(s(X),cons(Y,Z)) , Marked_sel(X,activate(Z))> 
     --> <Marked_sel(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_sel(X,activate(Z))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  sel(s(X),cons(Y,Z)) >= sel(X,activate(Z)) ;
  sel(0,cons(X,Z)) >= X ;
  sel(X1,X2) >= n__sel(X1,X2) ;
  activate(n__first(X1,X2)) >= first(X1,X2) ;
  activate(n__from(X)) >= from(X) ;
  activate(n__0) >= 0 ;
  activate(n__cons(X1,X2)) >= cons(X1,X2) ;
  activate(n__nil) >= nil ;
  activate(n__s(X)) >= s(X) ;
  activate(n__sel(X1,X2)) >= sel(X1,X2) ;
  activate(X) >= X ;
  s(X) >= n__s(X) ;
  cons(X1,X2) >= n__cons(X1,X2) ;
  0 >= n__0 ;
  nil >= n__nil ;
  first(s(X),cons(Y,Z)) >= cons(Y,n__first(X,activate(Z))) ;
  first(0,Z) >= nil ;
  first(X1,X2) >= n__first(X1,X2) ;
  from(X) >= cons(X,n__from(s(X))) ;
  from(X) >= n__from(X) ;
  sel1(s(X),cons(Y,Z)) >= sel1(X,activate(Z)) ;
  sel1(0,cons(X,Z)) >= quote(X) ;
  quote(n__0) >= 01 ;
  quote(n__s(X)) >= s1(quote(activate(X))) ;
  quote(n__sel(X,Z)) >= sel1(activate(X),activate(Z)) ;
  first1(s(X),cons(Y,Z)) >= cons1(quote(Y),first1(X,activate(Z))) ;
  first1(0,Z) >= nil1 ;
  quote1(n__first(X,Z)) >= first1(activate(X),activate(Z)) ;
  quote1(n__cons(X,Z)) >= cons1(quote(activate(X)),quote1(activate(Z))) ;
  quote1(n__nil) >= nil1 ;
  unquote(01) >= 0 ;
  unquote(s1(X)) >= s(unquote(X)) ;
  unquote1(nil1) >= nil ;
  unquote1(cons1(X,Z)) >= fcons(unquote(X),unquote1(Z)) ;
  fcons(X,Z) >= cons(X,Z) ;
  Marked_quote1(n__cons(X,Z)) >= Marked_quote1(activate(Z)) ;
 }
 + Disjunctions:{ 
{
  Marked_quote1(n__cons(X,Z)) > Marked_quote1(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 ===
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 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:
{
  sel(s(X),cons(Y,Z)) >= sel(X,activate(Z)) ;
  sel(0,cons(X,Z)) >= X ;
  sel(X1,X2) >= n__sel(X1,X2) ;
  activate(n__first(X1,X2)) >= first(X1,X2) ;
  activate(n__from(X)) >= from(X) ;
  activate(n__0) >= 0 ;
  activate(n__cons(X1,X2)) >= cons(X1,X2) ;
  activate(n__nil) >= nil ;
  activate(n__s(X)) >= s(X) ;
  activate(n__sel(X1,X2)) >= sel(X1,X2) ;
  activate(X) >= X ;
  s(X) >= n__s(X) ;
  cons(X1,X2) >= n__cons(X1,X2) ;
  0 >= n__0 ;
  nil >= n__nil ;
  first(s(X),cons(Y,Z)) >= cons(Y,n__first(X,activate(Z))) ;
  first(0,Z) >= nil ;
  first(X1,X2) >= n__first(X1,X2) ;
  from(X) >= cons(X,n__from(s(X))) ;
  from(X) >= n__from(X) ;
  sel1(s(X),cons(Y,Z)) >= sel1(X,activate(Z)) ;
  sel1(0,cons(X,Z)) >= quote(X) ;
  quote(n__0) >= 01 ;
  quote(n__s(X)) >= s1(quote(activate(X))) ;
  quote(n__sel(X,Z)) >= sel1(activate(X),activate(Z)) ;
  first1(s(X),cons(Y,Z)) >= cons1(quote(Y),first1(X,activate(Z))) ;
  first1(0,Z) >= nil1 ;
  quote1(n__first(X,Z)) >= first1(activate(X),activate(Z)) ;
  quote1(n__cons(X,Z)) >= cons1(quote(activate(X)),quote1(activate(Z))) ;
  quote1(n__nil) >= nil1 ;
  unquote(01) >= 0 ;
  unquote(s1(X)) >= s(unquote(X)) ;
  unquote1(nil1) >= nil ;
  unquote1(cons1(X,Z)) >= fcons(unquote(X),unquote1(Z)) ;
  fcons(X,Z) >= cons(X,Z) ;
  Marked_quote1(n__cons(X,Z)) > Marked_quote1(activate(Z)) ;
 }

APPLY CRITERIA (SOLVE_ORD)
Trying to solve the following constraints:
{
  sel(s(X),cons(Y,Z)) >= sel(X,activate(Z)) ;
  sel(0,cons(X,Z)) >= X ;
  sel(X1,X2) >= n__sel(X1,X2) ;
  activate(n__first(X1,X2)) >= first(X1,X2) ;
  activate(n__from(X)) >= from(X) ;
  activate(n__0) >= 0 ;
  activate(n__cons(X1,X2)) >= cons(X1,X2) ;
  activate(n__nil) >= nil ;
  activate(n__s(X)) >= s(X) ;
  activate(n__sel(X1,X2)) >= sel(X1,X2) ;
  activate(X) >= X ;
  s(X) >= n__s(X) ;
  cons(X1,X2) >= n__cons(X1,X2) ;
  0 >= n__0 ;
  nil >= n__nil ;
  first(s(X),cons(Y,Z)) >= cons(Y,n__first(X,activate(Z))) ;
  first(0,Z) >= nil ;
  first(X1,X2) >= n__first(X1,X2) ;
  from(X) >= cons(X,n__from(s(X))) ;
  from(X) >= n__from(X) ;
  sel1(s(X),cons(Y,Z)) >= sel1(X,activate(Z)) ;
  sel1(0,cons(X,Z)) >= quote(X) ;
  quote(n__0) >= 01 ;
  quote(n__s(X)) >= s1(quote(activate(X))) ;
  quote(n__sel(X,Z)) >= sel1(activate(X),activate(Z)) ;
  first1(s(X),cons(Y,Z)) >= cons1(quote(Y),first1(X,activate(Z))) ;
  first1(0,Z) >= nil1 ;
  quote1(n__first(X,Z)) >= first1(activate(X),activate(Z)) ;
  quote1(n__cons(X,Z)) >= cons1(quote(activate(X)),quote1(activate(Z))) ;
  quote1(n__nil) >= nil1 ;
  unquote(01) >= 0 ;
  unquote(s1(X)) >= s(unquote(X)) ;
  unquote1(nil1) >= nil ;
  unquote1(cons1(X,Z)) >= fcons(unquote(X),unquote1(Z)) ;
  fcons(X,Z) >= cons(X,Z) ;
  Marked_quote1(n__cons(X,Z)) > Marked_quote1(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 ===
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 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 52.581337 seconds (real time)
Cime Exit Status: 0