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

TRS termination of:
[1] terms(N) -> cons(recip(sqr(N)),terms(s(N)))
[2] sqr(0) -> 0
[3] sqr(s(X)) -> s(add(sqr(X),dbl(X)))
[4] dbl(0) -> 0
[5] dbl(s(X)) -> s(s(dbl(X)))
[6] add(0,X) -> X
[7] add(s(X),Y) -> s(add(X,Y))
[8] first(0,X) -> nil
[9] first(s(X),cons(Y,Z)) -> cons(Y,first(X,Z))
[10] half(0) -> 0
[11] half(s(0)) -> 0
[12] half(s(s(X))) -> s(half(X))
[13] half(dbl(X)) -> X


Sub problem: 
guided: 

DP termination of:
<Marked_terms(N) , Marked_sqr(N)>
<Marked_terms(N) , Marked_terms(s(N))>
<Marked_sqr(s(X)) , Marked_add(sqr(X),dbl(X))>
<Marked_sqr(s(X)) , Marked_sqr(X)>
<Marked_sqr(s(X)) , Marked_dbl(X)>
<Marked_dbl(s(X)) , Marked_dbl(X)>
<Marked_add(s(X),Y) , Marked_add(X,Y)>
<Marked_first(s(X),cons(Y,Z)) , Marked_first(X,Z)>
<Marked_half(s(s(X))) , Marked_half(X)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 6 components:

{  <Marked_terms(N) , Marked_terms(s(N))> 
      --> <Marked_terms(N) , Marked_terms(s(N))>
}

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

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

{  <Marked_add(s(X),Y) , Marked_add(X,Y)> 
      --> <Marked_add(s(X),Y) , Marked_add(X,Y)>
}

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

{  <Marked_half(s(s(X))) , Marked_half(X)> 
      --> <Marked_half(s(s(X))) , Marked_half(X)>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  sqr(s(X)) >= s(add(sqr(X),dbl(X))) ;
  sqr(0) >= 0 ;
  terms(N) >= cons(recip(sqr(N)),terms(s(N))) ;
  add(s(X),Y) >= s(add(X,Y)) ;
  add(0,X) >= X ;
  dbl(s(X)) >= s(s(dbl(X))) ;
  dbl(0) >= 0 ;
  first(s(X),cons(Y,Z)) >= cons(Y,first(X,Z)) ;
  first(0,X) >= nil ;
  half(s(s(X))) >= s(half(X)) ;
  half(s(0)) >= 0 ;
  half(0) >= 0 ;
  half(dbl(X)) >= X ;
  Marked_terms(N) >= Marked_terms(s(N)) ;
 }
 + Disjunctions:{ 
{
  Marked_terms(N) > Marked_terms(s(N)) ;
 }
 } 
=== 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:
{
  sqr(s(X)) >= s(add(sqr(X),dbl(X))) ;
  sqr(0) >= 0 ;
  terms(N) >= cons(recip(sqr(N)),terms(s(N))) ;
  add(s(X),Y) >= s(add(X,Y)) ;
  add(0,X) >= X ;
  dbl(s(X)) >= s(s(dbl(X))) ;
  dbl(0) >= 0 ;
  first(s(X),cons(Y,Z)) >= cons(Y,first(X,Z)) ;
  first(0,X) >= nil ;
  half(s(s(X))) >= s(half(X)) ;
  half(s(0)) >= 0 ;
  half(0) >= 0 ;
  half(dbl(X)) >= X ;
  Marked_terms(N) > Marked_terms(s(N)) ;
 }

APPLY CRITERIA (SOLVE_ORD)
Trying to solve the following constraints:
{
  sqr(s(X)) >= s(add(sqr(X),dbl(X))) ;
  sqr(0) >= 0 ;
  terms(N) >= cons(recip(sqr(N)),terms(s(N))) ;
  add(s(X),Y) >= s(add(X,Y)) ;
  add(0,X) >= X ;
  dbl(s(X)) >= s(s(dbl(X))) ;
  dbl(0) >= 0 ;
  first(s(X),cons(Y,Z)) >= cons(Y,first(X,Z)) ;
  first(0,X) >= nil ;
  half(s(s(X))) >= s(half(X)) ;
  half(s(0)) >= 0 ;
  half(0) >= 0 ;
  half(dbl(X)) >= X ;
  Marked_terms(N) > Marked_terms(s(N)) ;
 }
 + 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.(25 bt (40) [3])
=== 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 0.593067 seconds (real time)
Cime Exit Status: 0