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

TRS termination of:
[1] terms(N) -> cons(recip(sqr(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)) -> cons(Y)


Sub problem: 
guided: 

DP termination of:
<Marked_terms(N) , Marked_sqr(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)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 3 components:

{  <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)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  sqr(0) >= 0 ;
  sqr(s(X)) >= s(add(sqr(X),dbl(X))) ;
  terms(N) >= cons(recip(sqr(N))) ;
  add(0,X) >= X ;
  add(s(X),Y) >= s(add(X,Y)) ;
  dbl(0) >= 0 ;
  dbl(s(X)) >= s(s(dbl(X))) ;
  first(0,X) >= nil ;
  first(s(X),cons(Y)) >= cons(Y) ;
  Marked_sqr(s(X)) >= Marked_sqr(X) ;
 }
 + Disjunctions:{ 
{
  Marked_sqr(s(X)) > Marked_sqr(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 ===
=== STOPING TIMER virtual ===
constraint: sqr(0) >= 0
constraint: sqr(s(X)) >= s(add(sqr(X),dbl(X)))
constraint: terms(N) >= cons(recip(sqr(N)))
constraint: add(0,X) >= X
constraint: add(s(X),Y) >= s(add(X,Y))
constraint: dbl(0) >= 0
constraint: dbl(s(X)) >= s(s(dbl(X)))
constraint: first(0,X) >= nil
constraint: first(s(X),cons(Y)) >= cons(Y)
constraint: Marked_sqr(s(X)) >= Marked_sqr(X)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  sqr(0) >= 0 ;
  sqr(s(X)) >= s(add(sqr(X),dbl(X))) ;
  terms(N) >= cons(recip(sqr(N))) ;
  add(0,X) >= X ;
  add(s(X),Y) >= s(add(X,Y)) ;
  dbl(0) >= 0 ;
  dbl(s(X)) >= s(s(dbl(X))) ;
  first(0,X) >= nil ;
  first(s(X),cons(Y)) >= cons(Y) ;
  Marked_dbl(s(X)) >= Marked_dbl(X) ;
 }
 + Disjunctions:{ 
{
  Marked_dbl(s(X)) > Marked_dbl(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 ===
=== STOPING TIMER virtual ===
constraint: sqr(0) >= 0
constraint: sqr(s(X)) >= s(add(sqr(X),dbl(X)))
constraint: terms(N) >= cons(recip(sqr(N)))
constraint: add(0,X) >= X
constraint: add(s(X),Y) >= s(add(X,Y))
constraint: dbl(0) >= 0
constraint: dbl(s(X)) >= s(s(dbl(X)))
constraint: first(0,X) >= nil
constraint: first(s(X),cons(Y)) >= cons(Y)
constraint: Marked_dbl(s(X)) >= Marked_dbl(X)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  sqr(0) >= 0 ;
  sqr(s(X)) >= s(add(sqr(X),dbl(X))) ;
  terms(N) >= cons(recip(sqr(N))) ;
  add(0,X) >= X ;
  add(s(X),Y) >= s(add(X,Y)) ;
  dbl(0) >= 0 ;
  dbl(s(X)) >= s(s(dbl(X))) ;
  first(0,X) >= nil ;
  first(s(X),cons(Y)) >= cons(Y) ;
  Marked_add(s(X),Y) >= Marked_add(X,Y) ;
 }
 + Disjunctions:{ 
{
  Marked_add(s(X),Y) > Marked_add(X,Y) ;
 }
 } 
=== 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 ===
=== STOPING TIMER virtual ===
constraint: sqr(0) >= 0
constraint: sqr(s(X)) >= s(add(sqr(X),dbl(X)))
constraint: terms(N) >= cons(recip(sqr(N)))
constraint: add(0,X) >= X
constraint: add(s(X),Y) >= s(add(X,Y))
constraint: dbl(0) >= 0
constraint: dbl(s(X)) >= s(s(dbl(X)))
constraint: first(0,X) >= nil
constraint: first(s(X),cons(Y)) >= cons(Y)
constraint: Marked_add(s(X),Y) >= Marked_add(X,Y)
APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] terms(N) -> cons(recip(sqr(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)) -> cons(Y)
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_terms(N) , Marked_sqr(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)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_sqr(s(X)) , Marked_sqr(X)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     RPO with AFS = AFS: 
     and precedence:
     prec (All symbols are Lex.): { cons  <  terms ; recip  <  terms ;
                                   sqr  <  terms ; sqr  >  s ; sqr  >  add ;
                                   sqr  >  dbl ; terms  >  cons ;
                                   terms  >  recip ; terms  >  sqr ;
                                   terms  >  s ; terms  >  add ;
                                   terms  >  dbl ; s  <  sqr ; s  <  terms ;
                                   s  <  add ; s  <  dbl ; add  <  sqr ;
                                   add  <  terms ; add  >  s ; dbl  <  sqr ;
                                   dbl  <  terms ; dbl  >  s ; nil  <  first ;
                                   first  >  nil ; }

 ]} 
{
 
DP termination of:
<Marked_dbl(s(X)) , Marked_dbl(X)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     RPO with AFS = AFS: 
     and precedence:
     prec (All symbols are Lex.): { cons  <  terms ; recip  <  terms ;
                                   sqr  <  terms ; sqr  >  s ; sqr  >  add ;
                                   sqr  >  dbl ; terms  >  cons ;
                                   terms  >  recip ; terms  >  sqr ;
                                   terms  >  s ; terms  >  add ;
                                   terms  >  dbl ; s  <  sqr ; s  <  terms ;
                                   s  <  add ; s  <  dbl ; add  <  sqr ;
                                   add  <  terms ; add  >  s ; dbl  <  sqr ;
                                   dbl  <  terms ; dbl  >  s ; nil  <  first ;
                                   first  >  nil ; }

 ]} 
{
 
DP termination of:
<Marked_add(s(X),Y) , Marked_add(X,Y)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     RPO with AFS = AFS: 
     and precedence:
     prec (All symbols are Lex.): { cons  <  terms ; recip  <  terms ;
                                   sqr  <  terms ; sqr  >  s ; sqr  >  add ;
                                   sqr  >  dbl ; terms  >  cons ;
                                   terms  >  recip ; terms  >  sqr ;
                                   terms  >  s ; terms  >  add ;
                                   terms  >  dbl ; s  <  sqr ; s  <  terms ;
                                   s  <  add ; s  <  dbl ; add  <  sqr ;
                                   add  <  terms ; add  >  s ; dbl  <  sqr ;
                                   dbl  <  terms ; dbl  >  s ; nil  <  first ;
                                   first  >  nil ; }

 ]} 
 ]} 
 ]} 

Cime worked for 0.129798 seconds (real time)
Cime Exit Status: 0