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

TRS termination of:
[1] sqr(0) -> 0
[2] sqr(s(x)) -> +(sqr(x),s(double(x)))
[3] double(0) -> 0
[4] double(s(x)) -> s(s(double(x)))
[5] +(x,0) -> x
[6] +(x,s(y)) -> s(+(x,y))
[7] sqr(s(x)) -> s(+(sqr(x),double(x)))


Sub problem: 
guided: 

DP termination of:
<Marked_sqr(s(x)) , Marked_+(sqr(x),s(double(x)))>
<Marked_sqr(s(x)) , Marked_sqr(x)>
<Marked_sqr(s(x)) , Marked_double(x)>
<Marked_double(s(x)) , Marked_double(x)>
<Marked_+(x,s(y)) , Marked_+(x,y)>
<Marked_sqr(s(x)) , Marked_+(sqr(x),double(x))>
<Marked_sqr(s(x)) , Marked_sqr(x)>
<Marked_sqr(s(x)) , Marked_double(x)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 3 components:

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

{  <Marked_+(x,s(y)) , Marked_+(x,y)> --> <Marked_+(x,s(y)) , Marked_+(x,y)>
}

{  <Marked_double(s(x)) , Marked_double(x)> 
      --> <Marked_double(s(x)) , Marked_double(x)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  sqr(0) >= 0 ;
  sqr(s(x)) >= +(sqr(x),s(double(x))) ;
  sqr(s(x)) >= s(+(sqr(x),double(x))) ;
  +(x,0) >= x ;
  +(x,s(y)) >= s(+(x,y)) ;
  double(0) >= 0 ;
  double(s(x)) >= s(s(double(x))) ;
  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)) >= +(sqr(x),s(double(x)))
constraint: sqr(s(x)) >= s(+(sqr(x),double(x)))
constraint: +(x,0) >= x
constraint: +(x,s(y)) >= s(+(x,y))
constraint: double(0) >= 0
constraint: double(s(x)) >= s(s(double(x)))
constraint: Marked_sqr(s(x)) >= Marked_sqr(x)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  sqr(0) >= 0 ;
  sqr(s(x)) >= +(sqr(x),s(double(x))) ;
  sqr(s(x)) >= s(+(sqr(x),double(x))) ;
  +(x,0) >= x ;
  +(x,s(y)) >= s(+(x,y)) ;
  double(0) >= 0 ;
  double(s(x)) >= s(s(double(x))) ;
  Marked_+(x,s(y)) >= Marked_+(x,y) ;
 }
 + Disjunctions:{ 
{
  Marked_+(x,s(y)) > Marked_+(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)) >= +(sqr(x),s(double(x)))
constraint: sqr(s(x)) >= s(+(sqr(x),double(x)))
constraint: +(x,0) >= x
constraint: +(x,s(y)) >= s(+(x,y))
constraint: double(0) >= 0
constraint: double(s(x)) >= s(s(double(x)))
constraint: Marked_+(x,s(y)) >= Marked_+(x,y)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  sqr(0) >= 0 ;
  sqr(s(x)) >= +(sqr(x),s(double(x))) ;
  sqr(s(x)) >= s(+(sqr(x),double(x))) ;
  +(x,0) >= x ;
  +(x,s(y)) >= s(+(x,y)) ;
  double(0) >= 0 ;
  double(s(x)) >= s(s(double(x))) ;
  Marked_double(s(x)) >= Marked_double(x) ;
 }
 + Disjunctions:{ 
{
  Marked_double(s(x)) > Marked_double(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)) >= +(sqr(x),s(double(x)))
constraint: sqr(s(x)) >= s(+(sqr(x),double(x)))
constraint: +(x,0) >= x
constraint: +(x,s(y)) >= s(+(x,y))
constraint: double(0) >= 0
constraint: double(s(x)) >= s(s(double(x)))
constraint: Marked_double(s(x)) >= Marked_double(x)
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] sqr(0) -> 0
[2] sqr(s(x)) -> +(sqr(x),s(double(x)))
[3] double(0) -> 0
[4] double(s(x)) -> s(s(double(x)))
[5] +(x,0) -> x
[6] +(x,s(y)) -> s(+(x,y))
[7] sqr(s(x)) -> s(+(sqr(x),double(x)))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_sqr(s(x)) , Marked_+(sqr(x),s(double(x)))>
<Marked_sqr(s(x)) , Marked_sqr(x)>
<Marked_sqr(s(x)) , Marked_double(x)>
<Marked_double(s(x)) , Marked_double(x)>
<Marked_+(x,s(y)) , Marked_+(x,y)>
<Marked_sqr(s(x)) , Marked_+(sqr(x),double(x))>
<Marked_sqr(s(x)) , Marked_sqr(x)>
<Marked_sqr(s(x)) , Marked_double(x)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_sqr(s(x)) , Marked_sqr(x)>
<Marked_sqr(s(x)) , Marked_sqr(x)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     RPO with AFS = AFS: 
     and precedence:
     prec (All symbols are Lex.): { sqr  >  + ; sqr  >  s ; sqr  >  double ;
                                   +  <  sqr ; +  >  s ; s  <  sqr ; 
                                   s  <  + ; s  <  double ; double  <  sqr ;
                                   double  >  s ; }

 ]} 
{
 
DP termination of:
<Marked_+(x,s(y)) , Marked_+(x,y)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     RPO with AFS = AFS: 
     and precedence:
     prec (All symbols are Lex.): { sqr  >  + ; sqr  >  s ; sqr  >  double ;
                                   +  <  sqr ; +  >  s ; s  <  sqr ; 
                                   s  <  + ; s  <  double ; double  <  sqr ;
                                   double  >  s ; }

 ]} 
{
 
DP termination of:
<Marked_double(s(x)) , Marked_double(x)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     RPO with AFS = AFS: 
     and precedence:
     prec (All symbols are Lex.): { sqr  >  + ; sqr  >  s ; sqr  >  double ;
                                   +  <  sqr ; +  >  s ; s  <  sqr ; 
                                   s  <  + ; s  <  double ; double  <  sqr ;
                                   double  >  s ; }

 ]} 
 ]} 
 ]} 

Cime worked for 0.110796 seconds (real time)
Cime Exit Status: 0