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

TRS termination of:
[1] fac(0) -> 1
[2] fac(s(x)) ->  *(s(x),fac(x))
[3] floop(0,y) -> y
[4] floop(s(x),y) -> floop(x, *(s(x),y))
[5]  *(x,0) -> 0
[6]  *(x,s(y)) -> +( *(x,y),x)
[7] +(x,0) -> x
[8] +(x,s(y)) -> s(+(x,y))
[9] 1 -> s(0)
[10] fac(0) -> s(0)


Sub problem: 
guided: 

DP termination of:
<Marked_fac(0) , Marked_1>
<Marked_fac(s(x)) , Marked_*(s(x),fac(x))>
<Marked_fac(s(x)) , Marked_fac(x)>
<Marked_floop(s(x),y) , Marked_floop(x, *(s(x),y))>
<Marked_floop(s(x),y) , Marked_*(s(x),y)>
<Marked_*(x,s(y)) , Marked_+( *(x,y),x)>
<Marked_*(x,s(y)) , Marked_*(x,y)>
<Marked_+(x,s(y)) , Marked_+(x,y)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 4 components:

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

{  <Marked_floop(s(x),y) , Marked_floop(x, *(s(x),y))> 
      --> <Marked_floop(s(x),y) , Marked_floop(x, *(s(x),y))>
}

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

{  <Marked_+(x,s(y)) , Marked_+(x,y)> --> <Marked_+(x,s(y)) , Marked_+(x,y)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  1 >= s(0) ;
  fac(0) >= 1 ;
  fac(0) >= s(0) ;
  fac(s(x)) >=  *(s(x),fac(x)) ;
   *(x,0) >= 0 ;
   *(x,s(y)) >= +( *(x,y),x) ;
  floop(0,y) >= y ;
  floop(s(x),y) >= floop(x, *(s(x),y)) ;
  +(x,0) >= x ;
  +(x,s(y)) >= s(+(x,y)) ;
  Marked_fac(s(x)) >= Marked_fac(x) ;
 }
 + Disjunctions:{ 
{
  Marked_fac(s(x)) > Marked_fac(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: 1 >= s(0)
constraint: fac(0) >= 1
constraint: fac(0) >= s(0)
constraint: fac(s(x)) >=  *(s(x),fac(x))
constraint:  *(x,0) >= 0
constraint:  *(x,s(y)) >= +( *(x,y),x)
constraint: floop(0,y) >= y
constraint: floop(s(x),y) >= floop(x, *(s(x),y))
constraint: +(x,0) >= x
constraint: +(x,s(y)) >= s(+(x,y))
constraint: Marked_fac(s(x)) >= Marked_fac(x)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  1 >= s(0) ;
  fac(0) >= 1 ;
  fac(0) >= s(0) ;
  fac(s(x)) >=  *(s(x),fac(x)) ;
   *(x,0) >= 0 ;
   *(x,s(y)) >= +( *(x,y),x) ;
  floop(0,y) >= y ;
  floop(s(x),y) >= floop(x, *(s(x),y)) ;
  +(x,0) >= x ;
  +(x,s(y)) >= s(+(x,y)) ;
  Marked_floop(s(x),y) >= Marked_floop(x, *(s(x),y)) ;
 }
 + Disjunctions:{ 
{
  Marked_floop(s(x),y) > Marked_floop(x, *(s(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: 1 >= s(0)
constraint: fac(0) >= 1
constraint: fac(0) >= s(0)
constraint: fac(s(x)) >=  *(s(x),fac(x))
constraint:  *(x,0) >= 0
constraint:  *(x,s(y)) >= +( *(x,y),x)
constraint: floop(0,y) >= y
constraint: floop(s(x),y) >= floop(x, *(s(x),y))
constraint: +(x,0) >= x
constraint: +(x,s(y)) >= s(+(x,y))
constraint: Marked_floop(s(x),y) >= Marked_floop(x, *(s(x),y))
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  1 >= s(0) ;
  fac(0) >= 1 ;
  fac(0) >= s(0) ;
  fac(s(x)) >=  *(s(x),fac(x)) ;
   *(x,0) >= 0 ;
   *(x,s(y)) >= +( *(x,y),x) ;
  floop(0,y) >= y ;
  floop(s(x),y) >= floop(x, *(s(x),y)) ;
  +(x,0) >= x ;
  +(x,s(y)) >= s(+(x,y)) ;
  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: 1 >= s(0)
constraint: fac(0) >= 1
constraint: fac(0) >= s(0)
constraint: fac(s(x)) >=  *(s(x),fac(x))
constraint:  *(x,0) >= 0
constraint:  *(x,s(y)) >= +( *(x,y),x)
constraint: floop(0,y) >= y
constraint: floop(s(x),y) >= floop(x, *(s(x),y))
constraint: +(x,0) >= x
constraint: +(x,s(y)) >= s(+(x,y))
constraint: Marked_*(x,s(y)) >= Marked_*(x,y)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  1 >= s(0) ;
  fac(0) >= 1 ;
  fac(0) >= s(0) ;
  fac(s(x)) >=  *(s(x),fac(x)) ;
   *(x,0) >= 0 ;
   *(x,s(y)) >= +( *(x,y),x) ;
  floop(0,y) >= y ;
  floop(s(x),y) >= floop(x, *(s(x),y)) ;
  +(x,0) >= x ;
  +(x,s(y)) >= s(+(x,y)) ;
  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: 1 >= s(0)
constraint: fac(0) >= 1
constraint: fac(0) >= s(0)
constraint: fac(s(x)) >=  *(s(x),fac(x))
constraint:  *(x,0) >= 0
constraint:  *(x,s(y)) >= +( *(x,y),x)
constraint: floop(0,y) >= y
constraint: floop(s(x),y) >= floop(x, *(s(x),y))
constraint: +(x,0) >= x
constraint: +(x,s(y)) >= s(+(x,y))
constraint: Marked_+(x,s(y)) >= Marked_+(x,y)
APPLY CRITERIA (Graph splitting)
Found 0 components:
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] fac(0) -> 1
[2] fac(s(x)) ->  *(s(x),fac(x))
[3] floop(0,y) -> y
[4] floop(s(x),y) -> floop(x, *(s(x),y))
[5]  *(x,0) -> 0
[6]  *(x,s(y)) -> +( *(x,y),x)
[7] +(x,0) -> x
[8] +(x,s(y)) -> s(+(x,y))
[9] 1 -> s(0)
[10] fac(0) -> s(0)
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_fac(0) , Marked_1>
<Marked_fac(s(x)) , Marked_*(s(x),fac(x))>
<Marked_fac(s(x)) , Marked_fac(x)>
<Marked_floop(s(x),y) , Marked_floop(x, *(s(x),y))>
<Marked_floop(s(x),y) , Marked_*(s(x),y)>
<Marked_*(x,s(y)) , Marked_+( *(x,y),x)>
<Marked_*(x,s(y)) , Marked_*(x,y)>
<Marked_+(x,s(y)) , Marked_+(x,y)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_fac(s(x)) , Marked_fac(x)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     RPO with AFS = AFS: 
     and precedence:
     prec (All symbols are Lex.): { 1  <  fac ; 1  >  0 ; 1  >  s ; fac  >  1 ;
                                   fac  >  0 ; fac  >   * ; fac  >  s ;
                                   fac  >  + ; 0  <  1 ; 0  <  fac ;
                                    *  <  fac ;  *  >  s ;  *  <  floop ;
                                    *  >  + ; s  <  1 ; s  <  fac ; s  <   * ;
                                   s  <  floop ; s  <  + ; floop  >   * ;
                                   floop  >  s ; floop  >  + ; +  <  fac ;
                                   +  <   * ; +  >  s ; +  <  floop ; }

 ]} 
{
 
DP termination of:
<Marked_floop(s(x),y) , Marked_floop(x, *(s(x),y))>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     RPO with AFS = AFS: 
     and precedence:
     prec (All symbols are Lex.): { 1  <  fac ; 1  >  0 ; 1  >  s ; fac  >  1 ;
                                   fac  >  0 ; fac  >   * ; fac  >  s ;
                                   fac  >  + ; 0  <  1 ; 0  <  fac ;
                                    *  <  fac ;  *  >  s ;  *  <  floop ;
                                    *  >  + ;  *  <  Marked_floop ; s  <  1 ;
                                   s  <  fac ; s  <   * ; s  <  floop ;
                                   s  <  + ; s  <  Marked_floop ;
                                   floop  >   * ; floop  >  s ; floop  >  + ;
                                   +  <  fac ; +  <   * ; +  >  s ;
                                   +  <  floop ; +  <  Marked_floop ;
                                   Marked_floop  >   * ; Marked_floop  >  s ;
                                   Marked_floop  >  + ; }

 ]} 
{
 
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.): { 1  <  fac ; 1  >  0 ; 1  >  s ; fac  >  1 ;
                                   fac  >  0 ; fac  >   * ; fac  >  s ;
                                   fac  >  + ; 0  <  1 ; 0  <  fac ;
                                    *  <  fac ;  *  >  s ;  *  <  floop ;
                                    *  >  + ; s  <  1 ; s  <  fac ; s  <   * ;
                                   s  <  floop ; s  <  + ; floop  >   * ;
                                   floop  >  s ; floop  >  + ; +  <  fac ;
                                   +  <   * ; +  >  s ; +  <  floop ; }

 ]} 
{
 
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.): { 1  <  fac ; 1  >  0 ; 1  >  s ; fac  >  1 ;
                                   fac  >  0 ; fac  >   * ; fac  >  s ;
                                   fac  >  + ; 0  <  1 ; 0  <  fac ;
                                    *  <  fac ;  *  >  s ;  *  <  floop ;
                                    *  >  + ; s  <  1 ; s  <  fac ; s  <   * ;
                                   s  <  floop ; s  <  + ; floop  >   * ;
                                   floop  >  s ; floop  >  + ; +  <  fac ;
                                   +  <   * ; +  >  s ; +  <  floop ; }

 ]} 
 ]} 
 ]} 

Cime worked for 0.130001 seconds (real time)
Cime Exit Status: 0