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

TRS termination of:
[1] dbl(0) -> 0
[2] dbl(s(X)) -> s(s(dbl(X)))
[3] dbls(nil) -> nil
[4] dbls(cons(X,Y)) -> cons(dbl(X),dbls(Y))
[5] sel(0,cons(X,Y)) -> X
[6] sel(s(X),cons(Y,Z)) -> sel(X,Z)
[7] indx(nil,X) -> nil
[8] indx(cons(X,Y),Z) -> cons(sel(X,Z),indx(Y,Z))
[9] from(X) -> cons(X,from(s(X)))
[10] dbl1(0) -> 01
[11] dbl1(s(X)) -> s1(s1(dbl1(X)))
[12] sel1(0,cons(X,Y)) -> X
[13] sel1(s(X),cons(Y,Z)) -> sel1(X,Z)
[14] quote(0) -> 01
[15] quote(s(X)) -> s1(quote(X))
[16] quote(dbl(X)) -> dbl1(X)
[17] quote(sel(X,Y)) -> sel1(X,Y)


Sub problem: 
guided: 

DP termination of:
<Marked_dbl(s(X)) , Marked_dbl(X)>
<Marked_dbls(cons(X,Y)) , Marked_dbl(X)>
<Marked_dbls(cons(X,Y)) , Marked_dbls(Y)>
<Marked_sel(s(X),cons(Y,Z)) , Marked_sel(X,Z)>
<Marked_indx(cons(X,Y),Z) , Marked_sel(X,Z)>
<Marked_indx(cons(X,Y),Z) , Marked_indx(Y,Z)>
<Marked_from(X) , Marked_from(s(X))>
<Marked_dbl1(s(X)) , Marked_dbl1(X)>
<Marked_sel1(s(X),cons(Y,Z)) , Marked_sel1(X,Z)>
<Marked_quote(s(X)) , Marked_quote(X)>
<Marked_quote(dbl(X)) , Marked_dbl1(X)>
<Marked_quote(sel(X,Y)) , Marked_sel1(X,Y)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 8 components:

{  <Marked_dbls(cons(X,Y)) , Marked_dbls(Y)> 
      --> <Marked_dbls(cons(X,Y)) , Marked_dbls(Y)>
}

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

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

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

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

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

{  <Marked_dbl1(s(X)) , Marked_dbl1(X)> 
      --> <Marked_dbl1(s(X)) , Marked_dbl1(X)>
}

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

ST: Marked_dbls -> 1

APPLY CRITERIA (Subterm criterion)

ST: Marked_dbl -> 1

APPLY CRITERIA (Subterm criterion)

ST: Marked_indx -> 1

APPLY CRITERIA (Subterm criterion)

ST: Marked_sel -> 1

APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  dbl(0) >= 0 ;
  dbl(s(X)) >= s(s(dbl(X))) ;
  dbls(nil) >= nil ;
  dbls(cons(X,Y)) >= cons(dbl(X),dbls(Y)) ;
  sel(0,cons(X,Y)) >= X ;
  sel(s(X),cons(Y,Z)) >= sel(X,Z) ;
  indx(nil,X) >= nil ;
  indx(cons(X,Y),Z) >= cons(sel(X,Z),indx(Y,Z)) ;
  from(X) >= cons(X,from(s(X))) ;
  dbl1(0) >= 01 ;
  dbl1(s(X)) >= s1(s1(dbl1(X))) ;
  sel1(0,cons(X,Y)) >= X ;
  sel1(s(X),cons(Y,Z)) >= sel1(X,Z) ;
  quote(0) >= 01 ;
  quote(dbl(X)) >= dbl1(X) ;
  quote(s(X)) >= s1(quote(X)) ;
  quote(sel(X,Y)) >= sel1(X,Y) ;
  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:
{
  dbl(0) >= 0 ;
  dbl(s(X)) >= s(s(dbl(X))) ;
  dbls(nil) >= nil ;
  dbls(cons(X,Y)) >= cons(dbl(X),dbls(Y)) ;
  sel(0,cons(X,Y)) >= X ;
  sel(s(X),cons(Y,Z)) >= sel(X,Z) ;
  indx(nil,X) >= nil ;
  indx(cons(X,Y),Z) >= cons(sel(X,Z),indx(Y,Z)) ;
  from(X) >= cons(X,from(s(X))) ;
  dbl1(0) >= 01 ;
  dbl1(s(X)) >= s1(s1(dbl1(X))) ;
  sel1(0,cons(X,Y)) >= X ;
  sel1(s(X),cons(Y,Z)) >= sel1(X,Z) ;
  quote(0) >= 01 ;
  quote(dbl(X)) >= dbl1(X) ;
  quote(s(X)) >= s1(quote(X)) ;
  quote(sel(X,Y)) >= sel1(X,Y) ;
  Marked_from(X) > Marked_from(s(X)) ;
 }

APPLY CRITERIA (SOLVE_ORD)
Trying to solve the following constraints:
{
  dbl(0) >= 0 ;
  dbl(s(X)) >= s(s(dbl(X))) ;
  dbls(nil) >= nil ;
  dbls(cons(X,Y)) >= cons(dbl(X),dbls(Y)) ;
  sel(0,cons(X,Y)) >= X ;
  sel(s(X),cons(Y,Z)) >= sel(X,Z) ;
  indx(nil,X) >= nil ;
  indx(cons(X,Y),Z) >= cons(sel(X,Z),indx(Y,Z)) ;
  from(X) >= cons(X,from(s(X))) ;
  dbl1(0) >= 01 ;
  dbl1(s(X)) >= s1(s1(dbl1(X))) ;
  sel1(0,cons(X,Y)) >= X ;
  sel1(s(X),cons(Y,Z)) >= sel1(X,Z) ;
  quote(0) >= 01 ;
  quote(dbl(X)) >= dbl1(X) ;
  quote(s(X)) >= s1(quote(X)) ;
  quote(sel(X,Y)) >= sel1(X,Y) ;
  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.(1273 bt (1890) [117])
=== 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 0.619000 seconds (real time)
Cime Exit Status: 0