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

TRS termination of:
[1] sel(s(X),cons(Y,Z)) -> sel(X,Z)
[2] sel(0,cons(X,Z)) -> X
[3] first(0,Z) -> nil
[4] first(s(X),cons(Y,Z)) -> cons(Y,first(X,Z))
[5] from(X) -> cons(X,from(s(X)))
[6] sel1(s(X),cons(Y,Z)) -> sel1(X,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,Z))
[10] quote(0) -> 01
[11] quote1(cons(X,Z)) -> cons1(quote(X),quote1(Z))
[12] quote1(nil) -> nil1
[13] quote(s(X)) -> s1(quote(X))
[14] quote(sel(X,Z)) -> sel1(X,Z)
[15] quote1(first(X,Z)) -> first1(X,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)


Sub problem: 
guided: 

DP termination of:
<Marked_sel(s(X),cons(Y,Z)) , Marked_sel(X,Z)>
<Marked_first(s(X),cons(Y,Z)) , Marked_first(X,Z)>
<Marked_from(X) , Marked_from(s(X))>
<Marked_sel1(s(X),cons(Y,Z)) , Marked_sel1(X,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,Z)>
<Marked_quote1(cons(X,Z)) , Marked_quote(X)>
<Marked_quote1(cons(X,Z)) , Marked_quote1(Z)>
<Marked_quote(s(X)) , Marked_quote(X)>
<Marked_quote(sel(X,Z)) , Marked_sel1(X,Z)>
<Marked_quote1(first(X,Z)) , Marked_first1(X,Z)>
<Marked_unquote(s1(X)) , Marked_unquote(X)>
<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)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 8 components:

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

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

{  <Marked_from(X) , Marked_from(s(X))> 
      --> <Marked_from(X) , Marked_from(s(X))>
}

{  <Marked_quote1(cons(X,Z)) , Marked_quote1(Z)> 
      --> <Marked_quote1(cons(X,Z)) , Marked_quote1(Z)>
}

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

{  <Marked_quote(sel(X,Z)) , Marked_sel1(X,Z)> 
      --> <Marked_sel1(0,cons(X,Z)) , Marked_quote(X)>
  <Marked_quote(sel(X,Z)) , Marked_sel1(X,Z)> 
     --> <Marked_sel1(s(X),cons(Y,Z)) , Marked_sel1(X,Z)>
  <Marked_quote(s(X)) , Marked_quote(X)> 
     --> <Marked_quote(sel(X,Z)) , Marked_sel1(X,Z)>
  <Marked_quote(s(X)) , Marked_quote(X)> 
     --> <Marked_quote(s(X)) , Marked_quote(X)>
  <Marked_sel1(0,cons(X,Z)) , Marked_quote(X)> 
     --> <Marked_quote(sel(X,Z)) , Marked_sel1(X,Z)>
  <Marked_sel1(0,cons(X,Z)) , Marked_quote(X)> 
     --> <Marked_quote(s(X)) , Marked_quote(X)>
  <Marked_sel1(s(X),cons(Y,Z)) , Marked_sel1(X,Z)> 
     --> <Marked_sel1(0,cons(X,Z)) , Marked_quote(X)>
  <Marked_sel1(s(X),cons(Y,Z)) , Marked_sel1(X,Z)> 
     --> <Marked_sel1(s(X),cons(Y,Z)) , Marked_sel1(X,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)>
}
APPLY CRITERIA (Subterm criterion)

ST: Marked_sel -> 1

APPLY CRITERIA (Subterm criterion)

ST: Marked_first -> 1

APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  sel(s(X),cons(Y,Z)) >= sel(X,Z) ;
  sel(0,cons(X,Z)) >= X ;
  first(s(X),cons(Y,Z)) >= cons(Y,first(X,Z)) ;
  first(0,Z) >= nil ;
  from(X) >= cons(X,from(s(X))) ;
  sel1(s(X),cons(Y,Z)) >= sel1(X,Z) ;
  sel1(0,cons(X,Z)) >= quote(X) ;
  quote(sel(X,Z)) >= sel1(X,Z) ;
  quote(s(X)) >= s1(quote(X)) ;
  quote(0) >= 01 ;
  first1(s(X),cons(Y,Z)) >= cons1(quote(Y),first1(X,Z)) ;
  first1(0,Z) >= nil1 ;
  quote1(cons(X,Z)) >= cons1(quote(X),quote1(Z)) ;
  quote1(nil) >= nil1 ;
  quote1(first(X,Z)) >= first1(X,Z) ;
  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_from(X) >= Marked_from(s(X)) ;
 }
 + Disjunctions:{ 
{
  Marked_from(X) > Marked_from(s(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 ===
=== 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,Z) ;
  sel(0,cons(X,Z)) >= X ;
  first(s(X),cons(Y,Z)) >= cons(Y,first(X,Z)) ;
  first(0,Z) >= nil ;
  from(X) >= cons(X,from(s(X))) ;
  sel1(s(X),cons(Y,Z)) >= sel1(X,Z) ;
  sel1(0,cons(X,Z)) >= quote(X) ;
  quote(sel(X,Z)) >= sel1(X,Z) ;
  quote(s(X)) >= s1(quote(X)) ;
  quote(0) >= 01 ;
  first1(s(X),cons(Y,Z)) >= cons1(quote(Y),first1(X,Z)) ;
  first1(0,Z) >= nil1 ;
  quote1(cons(X,Z)) >= cons1(quote(X),quote1(Z)) ;
  quote1(nil) >= nil1 ;
  quote1(first(X,Z)) >= first1(X,Z) ;
  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_from(X) > Marked_from(s(X)) ;
 }

APPLY CRITERIA (SOLVE_ORD)
Trying to solve the following constraints:
{
  sel(s(X),cons(Y,Z)) >= sel(X,Z) ;
  sel(0,cons(X,Z)) >= X ;
  first(s(X),cons(Y,Z)) >= cons(Y,first(X,Z)) ;
  first(0,Z) >= nil ;
  from(X) >= cons(X,from(s(X))) ;
  sel1(s(X),cons(Y,Z)) >= sel1(X,Z) ;
  sel1(0,cons(X,Z)) >= quote(X) ;
  quote(sel(X,Z)) >= sel1(X,Z) ;
  quote(s(X)) >= s1(quote(X)) ;
  quote(0) >= 01 ;
  first1(s(X),cons(Y,Z)) >= cons1(quote(Y),first1(X,Z)) ;
  first1(0,Z) >= nil1 ;
  quote1(cons(X,Z)) >= cons1(quote(X),quote1(Z)) ;
  quote1(nil) >= nil1 ;
  quote1(first(X,Z)) >= first1(X,Z) ;
  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_from(X) > Marked_from(s(X)) ;
 }
 + Disjunctions:{ 
 } 
=== TIMER virtual : 10.000000 ===
Entering poly_solver
=== 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.(2110 bt (3087) [198])
=== TIMER virtual : 15.000000 ===
Entering poly_solver
=== 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
=== 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 0.678304 seconds (real time)
Cime Exit Status: 0