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

TRS termination of:
[1] app(app(and,true),true) -> true
[2] app(app(and,x),false) -> false
[3] app(app(and,false),y) -> false
[4] app(app(or,true),y) -> true
[5] app(app(or,x),true) -> true
[6] app(app(or,false),false) -> false
[7] app(app(forall,p),nil) -> true
[8] app(app(forall,p),app(app(cons,x),xs)) ->
 app(app(and,app(p,x)),app(app(forall,p),xs))
[9] app(app(forsome,p),nil) -> false
[10] app(app(forsome,p),app(app(cons,x),xs)) ->
 app(app(or,app(p,x)),app(app(forsome,p),xs))


Sub problem: 
guided: 

DP termination of:
<Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(app(and,app(p,x)),
                                                  app(app(forall,p),xs))>
<Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(and,app(p,x))>
<Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(p,x)>
<Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(app(forall,p),xs)>
<Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(app(or,app(p,x)),
                                                   app(app(forsome,p),xs))>
<Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(or,app(p,x))>
<Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(p,x)>
<Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(app(forsome,p),xs)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(app(forsome,p),
                                                      xs)> 
      --> <Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(
                                                             app(forsome,
                                                              p),xs)>
  <Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(app(forsome,p),
                                                     xs)> 
     --> <Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(p,x)>
  <Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(app(forsome,p),
                                                     xs)> 
     --> <Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(
                                                            app(or,app(p,x)),
                                                            app(app(forsome,p),
                                                             xs))>
  <Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(app(forsome,p),
                                                     xs)> 
     --> <Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(forall,
                                                            p),xs)>
  <Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(app(forsome,p),
                                                     xs)> 
     --> <Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(p,x)>
  <Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(app(forsome,p),
                                                     xs)> 
     --> <Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(and,app(p,x)),
                                                           app(app(forall,p),
                                                            xs))>
  <Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(p,x)> 
     --> <Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(
                                                            app(forsome,
                                                             p),xs)>
  <Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(p,x)> 
     --> <Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(p,x)>
  <Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(p,x)> 
     --> <Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(
                                                            app(or,app(p,x)),
                                                            app(app(forsome,p),
                                                             xs))>
  <Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(p,x)> 
     --> <Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(forall,
                                                            p),xs)>
  <Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(p,x)> 
     --> <Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(p,x)>
  <Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(p,x)> 
     --> <Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(and,app(p,x)),
                                                           app(app(forall,p),
                                                            xs))>
  <Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(app(or,app(p,x)),
                                                     app(app(forsome,p),xs))> 
     --> <Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(
                                                            app(forsome,
                                                             p),xs)>
  <Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(app(or,app(p,x)),
                                                     app(app(forsome,p),xs))> 
     --> <Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(p,x)>
  <Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(app(or,app(p,x)),
                                                     app(app(forsome,p),xs))> 
     --> <Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(
                                                            app(or,app(p,x)),
                                                            app(app(forsome,p),
                                                             xs))>
  <Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(app(or,app(p,x)),
                                                     app(app(forsome,p),xs))> 
     --> <Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(forall,
                                                            p),xs)>
  <Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(app(or,app(p,x)),
                                                     app(app(forsome,p),xs))> 
     --> <Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(p,x)>
  <Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(app(or,app(p,x)),
                                                     app(app(forsome,p),xs))> 
     --> <Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(and,app(p,x)),
                                                           app(app(forall,p),
                                                            xs))>
  <Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(app(forall,p),xs)> 
     --> <Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(
                                                            app(forsome,
                                                             p),xs)>
  <Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(app(forall,p),xs)> 
     --> <Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(p,x)>
  <Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(app(forall,p),xs)> 
     --> <Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(
                                                            app(or,app(p,x)),
                                                            app(app(forsome,p),
                                                             xs))>
  <Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(app(forall,p),xs)> 
     --> <Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(forall,
                                                            p),xs)>
  <Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(app(forall,p),xs)> 
     --> <Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(p,x)>
  <Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(app(forall,p),xs)> 
     --> <Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(and,app(p,x)),
                                                           app(app(forall,p),
                                                            xs))>
  <Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(p,x)> 
     --> <Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(
                                                            app(forsome,
                                                             p),xs)>
  <Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(p,x)> 
     --> <Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(p,x)>
  <Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(p,x)> 
     --> <Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(
                                                            app(or,app(p,x)),
                                                            app(app(forsome,p),
                                                             xs))>
  <Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(p,x)> 
     --> <Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(forall,
                                                            p),xs)>
  <Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(p,x)> 
     --> <Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(p,x)>
  <Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(p,x)> 
     --> <Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(and,app(p,x)),
                                                           app(app(forall,p),
                                                            xs))>
  <Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(app(and,app(p,x)),
                                                    app(app(forall,p),xs))> 
     --> <Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(
                                                            app(forsome,
                                                             p),xs)>
  <Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(app(and,app(p,x)),
                                                    app(app(forall,p),xs))> 
     --> <Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(p,x)>
  <Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(app(and,app(p,x)),
                                                    app(app(forall,p),xs))> 
     --> <Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(
                                                            app(or,app(p,x)),
                                                            app(app(forsome,p),
                                                             xs))>
  <Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(app(and,app(p,x)),
                                                    app(app(forall,p),xs))> 
     --> <Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(forall,
                                                            p),xs)>
  <Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(app(and,app(p,x)),
                                                    app(app(forall,p),xs))> 
     --> <Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(p,x)>
  <Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(app(and,app(p,x)),
                                                    app(app(forall,p),xs))> 
     --> <Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(and,app(p,x)),
                                                           app(app(forall,p),
                                                            xs))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  app(app(and,true),true) >= true ;
  app(app(and,false),y) >= false ;
  app(app(and,x),false) >= false ;
  app(app(or,true),y) >= true ;
  app(app(or,false),false) >= false ;
  app(app(or,x),true) >= true ;
  app(app(forall,p),app(app(cons,x),xs)) >= app(app(and,app(p,x)),
                                             app(app(forall,p),xs)) ;
  app(app(forall,p),nil) >= true ;
  app(app(forsome,p),app(app(cons,x),xs)) >= app(app(or,app(p,x)),
                                              app(app(forsome,p),xs)) ;
  app(app(forsome,p),nil) >= false ;
  Marked_app(app(forall,p),app(app(cons,x),xs)) >= Marked_app(app(and,app(p,x)),
                                                    app(app(forall,p),xs)) ;
  Marked_app(app(forall,p),app(app(cons,x),xs)) >= Marked_app(app(forall,p),xs) ;
  Marked_app(app(forall,p),app(app(cons,x),xs)) >= Marked_app(p,x) ;
  Marked_app(app(forsome,p),app(app(cons,x),xs)) >= Marked_app(app(or,app(p,x)),
                                                     app(app(forsome,p),xs)) ;
  Marked_app(app(forsome,p),app(app(cons,x),xs)) >= Marked_app(app(forsome,p),
                                                     xs) ;
  Marked_app(app(forsome,p),app(app(cons,x),xs)) >= Marked_app(p,x) ;
 }
 + Disjunctions:{ 
{
  Marked_app(app(forall,p),app(app(cons,x),xs)) > Marked_app(app(and,app(p,x)),
                                                   app(app(forall,p),xs)) ;
 }
{
  Marked_app(app(forall,p),app(app(cons,x),xs)) > Marked_app(app(forall,p),xs) ;
 }
{
  Marked_app(app(forall,p),app(app(cons,x),xs)) > Marked_app(p,x) ;
 }
{
  Marked_app(app(forsome,p),app(app(cons,x),xs)) > Marked_app(app(or,app(p,x)),
                                                    app(app(forsome,p),xs)) ;
 }
{
  Marked_app(app(forsome,p),app(app(cons,x),xs)) > Marked_app(app(forsome,p),
                                                    xs) ;
 }
{
  Marked_app(app(forsome,p),app(app(cons,x),xs)) > Marked_app(p,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 : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== 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
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: app(app(and,true),true) >= true
constraint: app(app(and,false),y) >= false
constraint: app(app(and,x),false) >= false
constraint: app(app(or,true),y) >= true
constraint: app(app(or,false),false) >= false
constraint: app(app(or,x),true) >= true
constraint: app(app(forall,p),app(app(cons,x),xs)) >= app(app(and,app(p,x)),
                                                       app(app(forall,p),xs))
constraint: app(app(forall,p),nil) >= true
constraint: app(app(forsome,p),app(app(cons,x),xs)) >= app(app(or,app(p,x)),
                                                        app(app(forsome,p),xs))
constraint: app(app(forsome,p),nil) >= false
constraint: Marked_app(app(forall,p),app(app(cons,x),xs)) >= Marked_app(
                                                              app(and,
                                                               app(p,x)),
                                                              app(app(forall,p),
                                                               xs))
constraint: Marked_app(app(forall,p),app(app(cons,x),xs)) >= Marked_app(
                                                              app(forall,
                                                               p),xs)
constraint: Marked_app(app(forall,p),app(app(cons,x),xs)) >= Marked_app(p,x)
constraint: Marked_app(app(forsome,p),app(app(cons,x),xs)) >= Marked_app(
                                                               app(or,
                                                                app(p,x)),
                                                               app(app(
                                                                    forsome,
                                                                    p),
                                                                xs))
constraint: Marked_app(app(forsome,p),app(app(cons,x),xs)) >= Marked_app(
                                                               app(forsome,
                                                                p),xs)
constraint: Marked_app(app(forsome,p),app(app(cons,x),xs)) >= Marked_app(p,x)
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(app(forsome,p),
                                                      xs)> 
      --> <Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(
                                                             app(forsome,
                                                              p),xs)>
  <Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(app(forsome,p),
                                                     xs)> 
     --> <Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(
                                                            app(or,app(p,x)),
                                                            app(app(forsome,p),
                                                             xs))>
  <Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(app(forsome,p),
                                                     xs)> 
     --> <Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(forall,
                                                            p),xs)>
  <Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(app(forsome,p),
                                                     xs)> 
     --> <Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(and,app(p,x)),
                                                           app(app(forall,p),
                                                            xs))>
  <Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(app(or,app(p,x)),
                                                     app(app(forsome,p),xs))> 
     --> <Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(
                                                            app(forsome,
                                                             p),xs)>
  <Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(app(or,app(p,x)),
                                                     app(app(forsome,p),xs))> 
     --> <Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(
                                                            app(or,app(p,x)),
                                                            app(app(forsome,p),
                                                             xs))>
  <Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(app(or,app(p,x)),
                                                     app(app(forsome,p),xs))> 
     --> <Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(forall,
                                                            p),xs)>
  <Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(app(or,app(p,x)),
                                                     app(app(forsome,p),xs))> 
     --> <Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(and,app(p,x)),
                                                           app(app(forall,p),
                                                            xs))>
  <Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(app(forall,p),xs)> 
     --> <Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(
                                                            app(forsome,
                                                             p),xs)>
  <Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(app(forall,p),xs)> 
     --> <Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(
                                                            app(or,app(p,x)),
                                                            app(app(forsome,p),
                                                             xs))>
  <Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(app(forall,p),xs)> 
     --> <Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(forall,
                                                            p),xs)>
  <Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(app(forall,p),xs)> 
     --> <Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(and,app(p,x)),
                                                           app(app(forall,p),
                                                            xs))>
  <Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(app(and,app(p,x)),
                                                    app(app(forall,p),xs))> 
     --> <Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(
                                                            app(forsome,
                                                             p),xs)>
  <Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(app(and,app(p,x)),
                                                    app(app(forall,p),xs))> 
     --> <Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(
                                                            app(or,app(p,x)),
                                                            app(app(forsome,p),
                                                             xs))>
  <Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(app(and,app(p,x)),
                                                    app(app(forall,p),xs))> 
     --> <Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(forall,
                                                            p),xs)>
  <Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(app(and,app(p,x)),
                                                    app(app(forall,p),xs))> 
     --> <Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(and,app(p,x)),
                                                           app(app(forall,p),
                                                            xs))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  app(app(and,true),true) >= true ;
  app(app(and,false),y) >= false ;
  app(app(and,x),false) >= false ;
  app(app(or,true),y) >= true ;
  app(app(or,false),false) >= false ;
  app(app(or,x),true) >= true ;
  app(app(forall,p),app(app(cons,x),xs)) >= app(app(and,app(p,x)),
                                             app(app(forall,p),xs)) ;
  app(app(forall,p),nil) >= true ;
  app(app(forsome,p),app(app(cons,x),xs)) >= app(app(or,app(p,x)),
                                              app(app(forsome,p),xs)) ;
  app(app(forsome,p),nil) >= false ;
  Marked_app(app(forall,p),app(app(cons,x),xs)) >= Marked_app(app(and,app(p,x)),
                                                    app(app(forall,p),xs)) ;
  Marked_app(app(forall,p),app(app(cons,x),xs)) >= Marked_app(app(forall,p),xs) ;
  Marked_app(app(forsome,p),app(app(cons,x),xs)) >= Marked_app(app(or,app(p,x)),
                                                     app(app(forsome,p),xs)) ;
  Marked_app(app(forsome,p),app(app(cons,x),xs)) >= Marked_app(app(forsome,p),
                                                     xs) ;
 }
 + Disjunctions:{ 
{
  Marked_app(app(forall,p),app(app(cons,x),xs)) > Marked_app(app(and,app(p,x)),
                                                   app(app(forall,p),xs)) ;
 }
{
  Marked_app(app(forall,p),app(app(cons,x),xs)) > Marked_app(app(forall,p),xs) ;
 }
{
  Marked_app(app(forsome,p),app(app(cons,x),xs)) > Marked_app(app(or,app(p,x)),
                                                    app(app(forsome,p),xs)) ;
 }
{
  Marked_app(app(forsome,p),app(app(cons,x),xs)) > Marked_app(app(forsome,p),
                                                    xs) ;
 }
 } 
=== 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
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: app(app(and,true),true) >= true
constraint: app(app(and,false),y) >= false
constraint: app(app(and,x),false) >= false
constraint: app(app(or,true),y) >= true
constraint: app(app(or,false),false) >= false
constraint: app(app(or,x),true) >= true
constraint: app(app(forall,p),app(app(cons,x),xs)) >= app(app(and,app(p,x)),
                                                       app(app(forall,p),xs))
constraint: app(app(forall,p),nil) >= true
constraint: app(app(forsome,p),app(app(cons,x),xs)) >= app(app(or,app(p,x)),
                                                        app(app(forsome,p),xs))
constraint: app(app(forsome,p),nil) >= false
constraint: Marked_app(app(forall,p),app(app(cons,x),xs)) >= Marked_app(
                                                              app(and,
                                                               app(p,x)),
                                                              app(app(forall,p),
                                                               xs))
constraint: Marked_app(app(forall,p),app(app(cons,x),xs)) >= Marked_app(
                                                              app(forall,
                                                               p),xs)
constraint: Marked_app(app(forsome,p),app(app(cons,x),xs)) >= Marked_app(
                                                               app(or,
                                                                app(p,x)),
                                                               app(app(
                                                                    forsome,
                                                                    p),
                                                                xs))
constraint: Marked_app(app(forsome,p),app(app(cons,x),xs)) >= Marked_app(
                                                               app(forsome,
                                                                p),xs)
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(app(or,
                                                                 app(p,x)),
                                                      app(app(forsome,p),xs))> 
      --> <Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(
                                                             app(or,app(p,x)),
                                                             app(app(forsome,p),
                                                              xs))>
  <Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(app(or,app(p,x)),
                                                     app(app(forsome,p),xs))> 
     --> <Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(and,app(p,x)),
                                                           app(app(forall,p),
                                                            xs))>
  <Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(app(and,app(p,x)),
                                                    app(app(forall,p),xs))> 
     --> <Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(
                                                            app(or,app(p,x)),
                                                            app(app(forsome,p),
                                                             xs))>
  <Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(app(and,app(p,x)),
                                                    app(app(forall,p),xs))> 
     --> <Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(and,app(p,x)),
                                                           app(app(forall,p),
                                                            xs))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  app(app(and,true),true) >= true ;
  app(app(and,false),y) >= false ;
  app(app(and,x),false) >= false ;
  app(app(or,true),y) >= true ;
  app(app(or,false),false) >= false ;
  app(app(or,x),true) >= true ;
  app(app(forall,p),app(app(cons,x),xs)) >= app(app(and,app(p,x)),
                                             app(app(forall,p),xs)) ;
  app(app(forall,p),nil) >= true ;
  app(app(forsome,p),app(app(cons,x),xs)) >= app(app(or,app(p,x)),
                                              app(app(forsome,p),xs)) ;
  app(app(forsome,p),nil) >= false ;
  Marked_app(app(forall,p),app(app(cons,x),xs)) >= Marked_app(app(and,app(p,x)),
                                                    app(app(forall,p),xs)) ;
  Marked_app(app(forsome,p),app(app(cons,x),xs)) >= Marked_app(app(or,app(p,x)),
                                                     app(app(forsome,p),xs)) ;
 }
 + Disjunctions:{ 
{
  Marked_app(app(forall,p),app(app(cons,x),xs)) > Marked_app(app(and,app(p,x)),
                                                   app(app(forall,p),xs)) ;
 }
{
  Marked_app(app(forsome,p),app(app(cons,x),xs)) > Marked_app(app(or,app(p,x)),
                                                    app(app(forsome,p),xs)) ;
 }
 } 
=== 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
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: app(app(and,true),true) >= true
constraint: app(app(and,false),y) >= false
constraint: app(app(and,x),false) >= false
constraint: app(app(or,true),y) >= true
constraint: app(app(or,false),false) >= false
constraint: app(app(or,x),true) >= true
constraint: app(app(forall,p),app(app(cons,x),xs)) >= app(app(and,app(p,x)),
                                                       app(app(forall,p),xs))
constraint: app(app(forall,p),nil) >= true
constraint: app(app(forsome,p),app(app(cons,x),xs)) >= app(app(or,app(p,x)),
                                                        app(app(forsome,p),xs))
constraint: app(app(forsome,p),nil) >= false
constraint: Marked_app(app(forall,p),app(app(cons,x),xs)) >= Marked_app(
                                                              app(and,
                                                               app(p,x)),
                                                              app(app(forall,p),
                                                               xs))
constraint: Marked_app(app(forsome,p),app(app(cons,x),xs)) >= Marked_app(
                                                               app(or,
                                                                app(p,x)),
                                                               app(app(
                                                                    forsome,
                                                                    p),
                                                                xs))
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] app(app(and,true),true) -> true
[2] app(app(and,x),false) -> false
[3] app(app(and,false),y) -> false
[4] app(app(or,true),y) -> true
[5] app(app(or,x),true) -> true
[6] app(app(or,false),false) -> false
[7] app(app(forall,p),nil) -> true
[8] app(app(forall,p),app(app(cons,x),xs)) ->
 app(app(and,app(p,x)),app(app(forall,p),xs))
[9] app(app(forsome,p),nil) -> false
[10] app(app(forsome,p),app(app(cons,x),xs)) ->
 app(app(or,app(p,x)),app(app(forsome,p),xs))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(app(
                                                                  and,
                                                                  app(p,x)),
                                                       app(app(forall,p),xs))>
<Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(and,app(p,x))>
<Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(p,x)>
<Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(app(forall,p),xs)>
<Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(app(or,app(p,x)),
                                                   app(app(forsome,p),xs))>
<Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(or,app(p,x))>
<Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(p,x)>
<Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(app(forsome,p),xs)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(app(
                                                                  and,
                                                                  app(p,x)),
                                                       app(app(forall,p),xs))>
<Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(p,x)>
<Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(app(forall,p),xs)>
<Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(app(or,app(p,x)),
                                                   app(app(forsome,p),xs))>
<Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(p,x)>
<Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(app(forsome,p),xs)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ true ] () = 0; 
 [ forsome ] () = 2; 
 [ or ] () = 0; 
 [ and ] () = 0; 
 [ nil ] () = 0; 
 [ app ] (X0,X1) = 2*X1*X0 + 1; 
 [ Marked_app ] (X0,X1) = 2*X0; 
 [ forall ] () = 1; 
 [ false ] () = 0; 
 [ cons ] () = 0; 
 removing <Marked_app(app(forall,p),app(app(cons,x),xs)),Marked_app(p,x)><
Marked_app(app(forsome,p),app(app(cons,x),xs)),Marked_app(p,x)>
 [ {
      
     DP termination of:
     <Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(app(
                                                                  and,
                                                                  app(p,x)),
                                                       app(app(forall,p),xs))>
<Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(app(forall,p),xs)>
<Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(app(or,app(p,x)),
                                                   app(app(forsome,p),xs))>
<Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(app(forsome,p),xs)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(app(
                                                                  and,
                                                                  app(p,x)),
                                                       app(app(forall,p),xs))>
<Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(app(forall,p),xs)>
<Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(app(or,app(p,x)),
                                                   app(app(forsome,p),xs))>
<Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(app(forsome,p),xs)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ true ] () = 0; 
 [ forsome ] () = 0; 
 [ or ] () = 0; 
 [ and ] () = 0; 
 [ nil ] () = 0; 
 [ app ] (X0,X1) = 1*X1 + 2; 
 [ Marked_app ] (X0,X1) = 2*X1; 
 [ forall ] () = 0; 
 [ false ] () = 0; 
 [ cons ] () = 0; 
 removing <Marked_app(app(forall,p),app(app(cons,x),xs)),Marked_app(app(
                                                                    forall,
                                                                    p),
                                                          xs)><Marked_app(
                                                                app(forsome,
                                                                 p),
                                                                app(app(cons,x),
                                                                 xs)),
Marked_app(app(forsome,p),xs)>
 [ {
      
     DP termination of:
     <Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(app(
                                                                  and,
                                                                  app(p,x)),
                                                       app(app(forall,p),xs))>
<Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(app(or,app(p,x)),
                                                   app(app(forsome,p),xs))>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_app(app(forall,p),app(app(cons,x),xs)) , Marked_app(app(
                                                                  and,
                                                                  app(p,x)),
                                                       app(app(forall,p),xs))>
<Marked_app(app(forsome,p),app(app(cons,x),xs)) , Marked_app(app(or,app(p,x)),
                                                   app(app(forsome,p),xs))>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ true ] () = 0; 
 [ forsome ] () = 0; 
 [ or ] () = 0; 
 [ and ] () = 1 + 0; 
 [ nil ] () = 0; 
 [ app ] (X0,X1) = 2*X0 + 0; 
 [ Marked_app ] (X0,X1) = 2*X0 + 3*X1 + 0; 
 [ forall ] () = 2 + 0; 
 [ false ] () = 0; 
 [ cons ] () = 2 + 0; 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 

Cime worked for 3.752846 seconds (real time)
Cime Exit Status: 0