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

TRS termination of:
[1] app(app(app(compose,f),g),x) -> app(g,app(f,x))
[2] app(reverse,l) -> app(app(reverse2,l),nil)
[3] app(app(reverse2,nil),l) -> l
[4] app(app(reverse2,app(app(cons,x),xs)),l) ->
 app(app(reverse2,xs),app(app(cons,x),l))
[5] app(hd,app(app(cons,x),xs)) -> x
[6] app(tl,app(app(cons,x),xs)) -> xs
[7] last -> app(app(compose,hd),reverse)
[8] init -> app(app(compose,reverse),app(app(compose,tl),reverse))


Sub problem: 
guided: 

DP termination of:
<Marked_app(app(app(compose,f),g),x) , Marked_app(g,app(f,x))>
<Marked_app(app(app(compose,f),g),x) , Marked_app(f,x)>
<Marked_app(reverse,l) , Marked_app(app(reverse2,l),nil)>
<Marked_app(reverse,l) , Marked_app(reverse2,l)>
<Marked_app(app(reverse2,app(app(cons,x),xs)),l) , Marked_app(app(reverse2,xs),
                                                    app(app(cons,x),l))>
<Marked_app(app(reverse2,app(app(cons,x),xs)),l) , Marked_app(reverse2,xs)>
<Marked_app(app(reverse2,app(app(cons,x),xs)),l) , Marked_app(app(cons,x),l)>
<Marked_last , Marked_app(app(compose,hd),reverse)>
<Marked_last , Marked_app(compose,hd)>
<Marked_init , Marked_app(app(compose,reverse),app(app(compose,tl),reverse))>
<Marked_init , Marked_app(compose,reverse)>
<Marked_init , Marked_app(app(compose,tl),reverse)>
<Marked_init , Marked_app(compose,tl)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_app(app(reverse2,app(app(cons,x),xs)),l) , Marked_app(app(cons,x),l)> 
      --> <Marked_app(app(reverse2,app(app(cons,x),xs)),l) , Marked_app(
                                                              app(cons,
                                                               x),l)>
  <Marked_app(app(reverse2,app(app(cons,x),xs)),l) , Marked_app(app(cons,x),l)> 
     --> <Marked_app(app(reverse2,app(app(cons,x),xs)),l) , Marked_app(
                                                             app(reverse2,
                                                              xs),
                                                             app(app(cons,x),l))>
  <Marked_app(app(reverse2,app(app(cons,x),xs)),l) , Marked_app(app(cons,x),l)> 
     --> <Marked_app(reverse,l) , Marked_app(app(reverse2,l),nil)>
  <Marked_app(app(reverse2,app(app(cons,x),xs)),l) , Marked_app(app(cons,x),l)> 
     --> <Marked_app(app(app(compose,f),g),x) , Marked_app(f,x)>
  <Marked_app(app(reverse2,app(app(cons,x),xs)),l) , Marked_app(app(cons,x),l)> 
     --> <Marked_app(app(app(compose,f),g),x) , Marked_app(g,app(f,x))>
  <Marked_app(app(reverse2,app(app(cons,x),xs)),l) , Marked_app(app(reverse2,
                                                                 xs),
                                                      app(app(cons,x),l))> 
     --> <Marked_app(app(reverse2,app(app(cons,x),xs)),l) , Marked_app(
                                                             app(cons,
                                                              x),l)>
  <Marked_app(app(reverse2,app(app(cons,x),xs)),l) , Marked_app(app(reverse2,
                                                                 xs),
                                                      app(app(cons,x),l))> 
     --> <Marked_app(app(reverse2,app(app(cons,x),xs)),l) , Marked_app(
                                                             app(reverse2,
                                                              xs),
                                                             app(app(cons,x),l))>
  <Marked_app(app(reverse2,app(app(cons,x),xs)),l) , Marked_app(app(reverse2,
                                                                 xs),
                                                      app(app(cons,x),l))> 
     --> <Marked_app(reverse,l) , Marked_app(app(reverse2,l),nil)>
  <Marked_app(app(reverse2,app(app(cons,x),xs)),l) , Marked_app(app(reverse2,
                                                                 xs),
                                                      app(app(cons,x),l))> 
     --> <Marked_app(app(app(compose,f),g),x) , Marked_app(f,x)>
  <Marked_app(app(reverse2,app(app(cons,x),xs)),l) , Marked_app(app(reverse2,
                                                                 xs),
                                                      app(app(cons,x),l))> 
     --> <Marked_app(app(app(compose,f),g),x) , Marked_app(g,app(f,x))>
  <Marked_app(reverse,l) , Marked_app(app(reverse2,l),nil)> 
     --> <Marked_app(app(reverse2,app(app(cons,x),xs)),l) , Marked_app(
                                                             app(cons,
                                                              x),l)>
  <Marked_app(reverse,l) , Marked_app(app(reverse2,l),nil)> 
     --> <Marked_app(app(reverse2,app(app(cons,x),xs)),l) , Marked_app(
                                                             app(reverse2,
                                                              xs),
                                                             app(app(cons,x),l))>
  <Marked_app(reverse,l) , Marked_app(app(reverse2,l),nil)> 
     --> <Marked_app(reverse,l) , Marked_app(app(reverse2,l),nil)>
  <Marked_app(reverse,l) , Marked_app(app(reverse2,l),nil)> 
     --> <Marked_app(app(app(compose,f),g),x) , Marked_app(f,x)>
  <Marked_app(reverse,l) , Marked_app(app(reverse2,l),nil)> 
     --> <Marked_app(app(app(compose,f),g),x) , Marked_app(g,app(f,x))>
  <Marked_app(app(app(compose,f),g),x) , Marked_app(f,x)> 
     --> <Marked_app(app(reverse2,app(app(cons,x),xs)),l) , Marked_app(
                                                             app(cons,
                                                              x),l)>
  <Marked_app(app(app(compose,f),g),x) , Marked_app(f,x)> 
     --> <Marked_app(app(reverse2,app(app(cons,x),xs)),l) , Marked_app(
                                                             app(reverse2,
                                                              xs),
                                                             app(app(cons,x),l))>
  <Marked_app(app(app(compose,f),g),x) , Marked_app(f,x)> 
     --> <Marked_app(reverse,l) , Marked_app(app(reverse2,l),nil)>
  <Marked_app(app(app(compose,f),g),x) , Marked_app(f,x)> 
     --> <Marked_app(app(app(compose,f),g),x) , Marked_app(f,x)>
  <Marked_app(app(app(compose,f),g),x) , Marked_app(f,x)> 
     --> <Marked_app(app(app(compose,f),g),x) , Marked_app(g,app(f,x))>
  <Marked_app(app(app(compose,f),g),x) , Marked_app(g,app(f,x))> 
     --> <Marked_app(app(reverse2,app(app(cons,x),xs)),l) , Marked_app(
                                                             app(cons,
                                                              x),l)>
  <Marked_app(app(app(compose,f),g),x) , Marked_app(g,app(f,x))> 
     --> <Marked_app(app(reverse2,app(app(cons,x),xs)),l) , Marked_app(
                                                             app(reverse2,
                                                              xs),
                                                             app(app(cons,x),l))>
  <Marked_app(app(app(compose,f),g),x) , Marked_app(g,app(f,x))> 
     --> <Marked_app(reverse,l) , Marked_app(app(reverse2,l),nil)>
  <Marked_app(app(app(compose,f),g),x) , Marked_app(g,app(f,x))> 
     --> <Marked_app(app(app(compose,f),g),x) , Marked_app(f,x)>
  <Marked_app(app(app(compose,f),g),x) , Marked_app(g,app(f,x))> 
     --> <Marked_app(app(app(compose,f),g),x) , Marked_app(g,app(f,x))>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  app(app(app(compose,f),g),x) >= app(g,app(f,x)) ;
  app(app(reverse2,app(app(cons,x),xs)),l) >= app(app(reverse2,xs),
                                               app(app(cons,x),l)) ;
  app(app(reverse2,nil),l) >= l ;
  app(reverse,l) >= app(app(reverse2,l),nil) ;
  app(hd,app(app(cons,x),xs)) >= x ;
  app(tl,app(app(cons,x),xs)) >= xs ;
  last >= app(app(compose,hd),reverse) ;
  init >= app(app(compose,reverse),app(app(compose,tl),reverse)) ;
  Marked_app(app(app(compose,f),g),x) >= Marked_app(f,x) ;
  Marked_app(app(app(compose,f),g),x) >= Marked_app(g,app(f,x)) ;
  Marked_app(app(reverse2,app(app(cons,x),xs)),l) >= Marked_app(app(reverse2,
                                                                 xs),
                                                      app(app(cons,x),l)) ;
  Marked_app(app(reverse2,app(app(cons,x),xs)),l) >= Marked_app(app(cons,x),l) ;
  Marked_app(reverse,l) >= Marked_app(app(reverse2,l),nil) ;
 }
 + Disjunctions:{ 
{
  Marked_app(app(app(compose,f),g),x) > Marked_app(f,x) ;
 }
{
  Marked_app(app(app(compose,f),g),x) > Marked_app(g,app(f,x)) ;
 }
{
  Marked_app(app(reverse2,app(app(cons,x),xs)),l) > Marked_app(app(reverse2,xs),
                                                     app(app(cons,x),l)) ;
 }
{
  Marked_app(app(reverse2,app(app(cons,x),xs)),l) > Marked_app(app(cons,x),l) ;
 }
{
  Marked_app(reverse,l) > Marked_app(app(reverse2,l),nil) ;
 }
 } 
=== 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(app(compose,f),g),x) >= app(g,app(f,x))
constraint: app(app(reverse2,app(app(cons,x),xs)),l) >= app(app(reverse2,xs),
                                                         app(app(cons,x),l))
constraint: app(app(reverse2,nil),l) >= l
constraint: app(reverse,l) >= app(app(reverse2,l),nil)
constraint: app(hd,app(app(cons,x),xs)) >= x
constraint: app(tl,app(app(cons,x),xs)) >= xs
constraint: last >= app(app(compose,hd),reverse)
constraint: init >= app(app(compose,reverse),app(app(compose,tl),reverse))
constraint: Marked_app(app(app(compose,f),g),x) >= Marked_app(f,x)
constraint: Marked_app(app(app(compose,f),g),x) >= Marked_app(g,app(f,x))
constraint: Marked_app(app(reverse2,app(app(cons,x),xs)),l) >= Marked_app(
                                                                app(reverse2,
                                                                 xs),
                                                                app(app(cons,x),
                                                                 l))
constraint: Marked_app(app(reverse2,app(app(cons,x),xs)),l) >= Marked_app(
                                                                app(cons,
                                                                 x),l)
constraint: Marked_app(reverse,l) >= Marked_app(app(reverse2,l),nil)
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_app(app(reverse2,app(app(cons,x),xs)),l) , Marked_app(app(cons,x),l)> 
      --> <Marked_app(app(reverse2,app(app(cons,x),xs)),l) , Marked_app(
                                                              app(cons,
                                                               x),l)>
  <Marked_app(app(reverse2,app(app(cons,x),xs)),l) , Marked_app(app(cons,x),l)> 
     --> <Marked_app(app(reverse2,app(app(cons,x),xs)),l) , Marked_app(
                                                             app(reverse2,
                                                              xs),
                                                             app(app(cons,x),l))>
  <Marked_app(app(reverse2,app(app(cons,x),xs)),l) , Marked_app(app(cons,x),l)> 
     --> <Marked_app(app(app(compose,f),g),x) , Marked_app(f,x)>
  <Marked_app(app(reverse2,app(app(cons,x),xs)),l) , Marked_app(app(cons,x),l)> 
     --> <Marked_app(app(app(compose,f),g),x) , Marked_app(g,app(f,x))>
  <Marked_app(app(reverse2,app(app(cons,x),xs)),l) , Marked_app(app(reverse2,
                                                                 xs),
                                                      app(app(cons,x),l))> 
     --> <Marked_app(app(reverse2,app(app(cons,x),xs)),l) , Marked_app(
                                                             app(cons,
                                                              x),l)>
  <Marked_app(app(reverse2,app(app(cons,x),xs)),l) , Marked_app(app(reverse2,
                                                                 xs),
                                                      app(app(cons,x),l))> 
     --> <Marked_app(app(reverse2,app(app(cons,x),xs)),l) , Marked_app(
                                                             app(reverse2,
                                                              xs),
                                                             app(app(cons,x),l))>
  <Marked_app(app(reverse2,app(app(cons,x),xs)),l) , Marked_app(app(reverse2,
                                                                 xs),
                                                      app(app(cons,x),l))> 
     --> <Marked_app(app(app(compose,f),g),x) , Marked_app(f,x)>
  <Marked_app(app(reverse2,app(app(cons,x),xs)),l) , Marked_app(app(reverse2,
                                                                 xs),
                                                      app(app(cons,x),l))> 
     --> <Marked_app(app(app(compose,f),g),x) , Marked_app(g,app(f,x))>
  <Marked_app(app(app(compose,f),g),x) , Marked_app(f,x)> 
     --> <Marked_app(app(reverse2,app(app(cons,x),xs)),l) , Marked_app(
                                                             app(cons,
                                                              x),l)>
  <Marked_app(app(app(compose,f),g),x) , Marked_app(f,x)> 
     --> <Marked_app(app(reverse2,app(app(cons,x),xs)),l) , Marked_app(
                                                             app(reverse2,
                                                              xs),
                                                             app(app(cons,x),l))>
  <Marked_app(app(app(compose,f),g),x) , Marked_app(f,x)> 
     --> <Marked_app(app(app(compose,f),g),x) , Marked_app(f,x)>
  <Marked_app(app(app(compose,f),g),x) , Marked_app(f,x)> 
     --> <Marked_app(app(app(compose,f),g),x) , Marked_app(g,app(f,x))>
  <Marked_app(app(app(compose,f),g),x) , Marked_app(g,app(f,x))> 
     --> <Marked_app(app(reverse2,app(app(cons,x),xs)),l) , Marked_app(
                                                             app(cons,
                                                              x),l)>
  <Marked_app(app(app(compose,f),g),x) , Marked_app(g,app(f,x))> 
     --> <Marked_app(app(reverse2,app(app(cons,x),xs)),l) , Marked_app(
                                                             app(reverse2,
                                                              xs),
                                                             app(app(cons,x),l))>
  <Marked_app(app(app(compose,f),g),x) , Marked_app(g,app(f,x))> 
     --> <Marked_app(app(app(compose,f),g),x) , Marked_app(f,x)>
  <Marked_app(app(app(compose,f),g),x) , Marked_app(g,app(f,x))> 
     --> <Marked_app(app(app(compose,f),g),x) , Marked_app(g,app(f,x))>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  app(app(app(compose,f),g),x) >= app(g,app(f,x)) ;
  app(app(reverse2,app(app(cons,x),xs)),l) >= app(app(reverse2,xs),
                                               app(app(cons,x),l)) ;
  app(app(reverse2,nil),l) >= l ;
  app(reverse,l) >= app(app(reverse2,l),nil) ;
  app(hd,app(app(cons,x),xs)) >= x ;
  app(tl,app(app(cons,x),xs)) >= xs ;
  last >= app(app(compose,hd),reverse) ;
  init >= app(app(compose,reverse),app(app(compose,tl),reverse)) ;
  Marked_app(app(app(compose,f),g),x) >= Marked_app(f,x) ;
  Marked_app(app(app(compose,f),g),x) >= Marked_app(g,app(f,x)) ;
  Marked_app(app(reverse2,app(app(cons,x),xs)),l) >= Marked_app(app(reverse2,
                                                                 xs),
                                                      app(app(cons,x),l)) ;
  Marked_app(app(reverse2,app(app(cons,x),xs)),l) >= Marked_app(app(cons,x),l) ;
 }
 + Disjunctions:{ 
{
  Marked_app(app(app(compose,f),g),x) > Marked_app(f,x) ;
 }
{
  Marked_app(app(app(compose,f),g),x) > Marked_app(g,app(f,x)) ;
 }
{
  Marked_app(app(reverse2,app(app(cons,x),xs)),l) > Marked_app(app(reverse2,xs),
                                                     app(app(cons,x),l)) ;
 }
{
  Marked_app(app(reverse2,app(app(cons,x),xs)),l) > Marked_app(app(cons,x),l) ;
 }
 } 
=== 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(app(compose,f),g),x) >= app(g,app(f,x))
constraint: app(app(reverse2,app(app(cons,x),xs)),l) >= app(app(reverse2,xs),
                                                         app(app(cons,x),l))
constraint: app(app(reverse2,nil),l) >= l
constraint: app(reverse,l) >= app(app(reverse2,l),nil)
constraint: app(hd,app(app(cons,x),xs)) >= x
constraint: app(tl,app(app(cons,x),xs)) >= xs
constraint: last >= app(app(compose,hd),reverse)
constraint: init >= app(app(compose,reverse),app(app(compose,tl),reverse))
constraint: Marked_app(app(app(compose,f),g),x) >= Marked_app(f,x)
constraint: Marked_app(app(app(compose,f),g),x) >= Marked_app(g,app(f,x))
constraint: Marked_app(app(reverse2,app(app(cons,x),xs)),l) >= Marked_app(
                                                                app(reverse2,
                                                                 xs),
                                                                app(app(cons,x),
                                                                 l))
constraint: Marked_app(app(reverse2,app(app(cons,x),xs)),l) >= Marked_app(
                                                                app(cons,
                                                                 x),l)
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_app(app(reverse2,app(app(cons,x),xs)),l) , Marked_app(app(cons,x),l)> 
      --> <Marked_app(app(reverse2,app(app(cons,x),xs)),l) , Marked_app(
                                                              app(cons,
                                                               x),l)>
  <Marked_app(app(reverse2,app(app(cons,x),xs)),l) , Marked_app(app(cons,x),l)> 
     --> <Marked_app(app(app(compose,f),g),x) , Marked_app(f,x)>
  <Marked_app(app(reverse2,app(app(cons,x),xs)),l) , Marked_app(app(cons,x),l)> 
     --> <Marked_app(app(app(compose,f),g),x) , Marked_app(g,app(f,x))>
  <Marked_app(app(app(compose,f),g),x) , Marked_app(f,x)> 
     --> <Marked_app(app(reverse2,app(app(cons,x),xs)),l) , Marked_app(
                                                             app(cons,
                                                              x),l)>
  <Marked_app(app(app(compose,f),g),x) , Marked_app(f,x)> 
     --> <Marked_app(app(app(compose,f),g),x) , Marked_app(f,x)>
  <Marked_app(app(app(compose,f),g),x) , Marked_app(f,x)> 
     --> <Marked_app(app(app(compose,f),g),x) , Marked_app(g,app(f,x))>
  <Marked_app(app(app(compose,f),g),x) , Marked_app(g,app(f,x))> 
     --> <Marked_app(app(reverse2,app(app(cons,x),xs)),l) , Marked_app(
                                                             app(cons,
                                                              x),l)>
  <Marked_app(app(app(compose,f),g),x) , Marked_app(g,app(f,x))> 
     --> <Marked_app(app(app(compose,f),g),x) , Marked_app(f,x)>
  <Marked_app(app(app(compose,f),g),x) , Marked_app(g,app(f,x))> 
     --> <Marked_app(app(app(compose,f),g),x) , Marked_app(g,app(f,x))>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  app(app(app(compose,f),g),x) >= app(g,app(f,x)) ;
  app(app(reverse2,app(app(cons,x),xs)),l) >= app(app(reverse2,xs),
                                               app(app(cons,x),l)) ;
  app(app(reverse2,nil),l) >= l ;
  app(reverse,l) >= app(app(reverse2,l),nil) ;
  app(hd,app(app(cons,x),xs)) >= x ;
  app(tl,app(app(cons,x),xs)) >= xs ;
  last >= app(app(compose,hd),reverse) ;
  init >= app(app(compose,reverse),app(app(compose,tl),reverse)) ;
  Marked_app(app(app(compose,f),g),x) >= Marked_app(f,x) ;
  Marked_app(app(app(compose,f),g),x) >= Marked_app(g,app(f,x)) ;
  Marked_app(app(reverse2,app(app(cons,x),xs)),l) >= Marked_app(app(cons,x),l) ;
 }
 + Disjunctions:{ 
{
  Marked_app(app(app(compose,f),g),x) > Marked_app(f,x) ;
 }
{
  Marked_app(app(app(compose,f),g),x) > Marked_app(g,app(f,x)) ;
 }
{
  Marked_app(app(reverse2,app(app(cons,x),xs)),l) > Marked_app(app(cons,x),l) ;
 }
 } 
=== 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(app(compose,f),g),x) >= app(g,app(f,x))
constraint: app(app(reverse2,app(app(cons,x),xs)),l) >= app(app(reverse2,xs),
                                                         app(app(cons,x),l))
constraint: app(app(reverse2,nil),l) >= l
constraint: app(reverse,l) >= app(app(reverse2,l),nil)
constraint: app(hd,app(app(cons,x),xs)) >= x
constraint: app(tl,app(app(cons,x),xs)) >= xs
constraint: last >= app(app(compose,hd),reverse)
constraint: init >= app(app(compose,reverse),app(app(compose,tl),reverse))
constraint: Marked_app(app(app(compose,f),g),x) >= Marked_app(f,x)
constraint: Marked_app(app(app(compose,f),g),x) >= Marked_app(g,app(f,x))
constraint: Marked_app(app(reverse2,app(app(cons,x),xs)),l) >= Marked_app(
                                                                app(cons,
                                                                 x),l)
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_app(app(app(compose,f),g),x) , Marked_app(f,x)> 
      --> <Marked_app(app(app(compose,f),g),x) , Marked_app(f,x)>
  <Marked_app(app(app(compose,f),g),x) , Marked_app(f,x)> 
     --> <Marked_app(app(app(compose,f),g),x) , Marked_app(g,app(f,x))>
  <Marked_app(app(app(compose,f),g),x) , Marked_app(g,app(f,x))> 
     --> <Marked_app(app(app(compose,f),g),x) , Marked_app(f,x)>
  <Marked_app(app(app(compose,f),g),x) , Marked_app(g,app(f,x))> 
     --> <Marked_app(app(app(compose,f),g),x) , Marked_app(g,app(f,x))>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  app(app(app(compose,f),g),x) >= app(g,app(f,x)) ;
  app(app(reverse2,app(app(cons,x),xs)),l) >= app(app(reverse2,xs),
                                               app(app(cons,x),l)) ;
  app(app(reverse2,nil),l) >= l ;
  app(reverse,l) >= app(app(reverse2,l),nil) ;
  app(hd,app(app(cons,x),xs)) >= x ;
  app(tl,app(app(cons,x),xs)) >= xs ;
  last >= app(app(compose,hd),reverse) ;
  init >= app(app(compose,reverse),app(app(compose,tl),reverse)) ;
  Marked_app(app(app(compose,f),g),x) >= Marked_app(f,x) ;
  Marked_app(app(app(compose,f),g),x) >= Marked_app(g,app(f,x)) ;
 }
 + Disjunctions:{ 
{
  Marked_app(app(app(compose,f),g),x) > Marked_app(f,x) ;
 }
{
  Marked_app(app(app(compose,f),g),x) > Marked_app(g,app(f,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
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: app(app(app(compose,f),g),x) >= app(g,app(f,x))
constraint: app(app(reverse2,app(app(cons,x),xs)),l) >= app(app(reverse2,xs),
                                                         app(app(cons,x),l))
constraint: app(app(reverse2,nil),l) >= l
constraint: app(reverse,l) >= app(app(reverse2,l),nil)
constraint: app(hd,app(app(cons,x),xs)) >= x
constraint: app(tl,app(app(cons,x),xs)) >= xs
constraint: last >= app(app(compose,hd),reverse)
constraint: init >= app(app(compose,reverse),app(app(compose,tl),reverse))
constraint: Marked_app(app(app(compose,f),g),x) >= Marked_app(f,x)
constraint: Marked_app(app(app(compose,f),g),x) >= Marked_app(g,app(f,x))
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] app(app(app(compose,f),g),x) -> app(g,app(f,x))
[2] app(reverse,l) -> app(app(reverse2,l),nil)
[3] app(app(reverse2,nil),l) -> l
[4] app(app(reverse2,app(app(cons,x),xs)),l) ->
 app(app(reverse2,xs),app(app(cons,x),l))
[5] app(hd,app(app(cons,x),xs)) -> x
[6] app(tl,app(app(cons,x),xs)) -> xs
[7] last -> app(app(compose,hd),reverse)
[8] init -> app(app(compose,reverse),app(app(compose,tl),reverse))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_app(app(app(compose,f),g),x) , Marked_app(g,app(f,x))>
<Marked_app(app(app(compose,f),g),x) , Marked_app(f,x)>
<Marked_app(reverse,l) , Marked_app(app(reverse2,l),nil)>
<Marked_app(reverse,l) , Marked_app(reverse2,l)>
<Marked_app(app(reverse2,app(app(cons,x),xs)),l) , Marked_app(app(reverse2,xs),
                                                    app(app(cons,x),l))>
<Marked_app(app(reverse2,app(app(cons,x),xs)),l) , Marked_app(reverse2,xs)>
<Marked_app(app(reverse2,app(app(cons,x),xs)),l) , Marked_app(app(cons,x),l)>
<Marked_last , Marked_app(app(compose,hd),reverse)>
<Marked_last , Marked_app(compose,hd)>
<Marked_init , Marked_app(app(compose,reverse),app(app(compose,tl),reverse))>
<Marked_init , Marked_app(compose,reverse)>
<Marked_init , Marked_app(app(compose,tl),reverse)>
<Marked_init , Marked_app(compose,tl)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_app(app(app(compose,f),g),x) , Marked_app(g,app(f,x))>
<Marked_app(app(app(compose,f),g),x) , Marked_app(f,x)>
<Marked_app(reverse,l) , Marked_app(app(reverse2,l),nil)>
<Marked_app(app(reverse2,app(app(cons,x),xs)),l) , Marked_app(app(reverse2,xs),
                                                    app(app(cons,x),l))>
<Marked_app(app(reverse2,app(app(cons,x),xs)),l) , Marked_app(app(cons,x),l)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ app ] (X0,X1) = 1*X1 + 1*X0; 
 [ last ] () = 3; 
 [ reverse ] () = 1; 
 [ reverse2 ] () = 0; 
 [ hd ] () = 1; 
 [ compose ] () = 0; 
 [ init ] () = 3; 
 [ cons ] () = 0; 
 [ nil ] () = 0; 
 [ Marked_app ] (X0,X1) = 2*X1 + 2*X0; 
 [ tl ] () = 0; 
 removing <Marked_app(reverse,l),Marked_app(app(reverse2,l),nil)>
 [ {
      
     DP termination of:
     <Marked_app(app(app(compose,f),g),x) , Marked_app(g,app(f,x))>
<Marked_app(app(app(compose,f),g),x) , Marked_app(f,x)>
<Marked_app(app(reverse2,app(app(cons,x),xs)),l) , Marked_app(app(reverse2,xs),
                                                    app(app(cons,x),l))>
<Marked_app(app(reverse2,app(app(cons,x),xs)),l) , Marked_app(app(cons,x),l)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_app(app(app(compose,f),g),x) , Marked_app(g,app(f,x))>
<Marked_app(app(app(compose,f),g),x) , Marked_app(f,x)>
<Marked_app(app(reverse2,app(app(cons,x),xs)),l) , Marked_app(app(reverse2,xs),
                                                    app(app(cons,x),l))>
<Marked_app(app(reverse2,app(app(cons,x),xs)),l) , Marked_app(app(cons,x),l)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ app ] (X0,X1) = 1*X1 + 1*X0; 
 [ last ] () = 1; 
 [ reverse ] () = 0; 
 [ reverse2 ] () = 0; 
 [ hd ] () = 0; 
 [ compose ] () = 0; 
 [ init ] () = 1; 
 [ cons ] () = 2; 
 [ nil ] () = 0; 
 [ Marked_app ] (X0,X1) = 1*X0; 
 [ tl ] () = 0; 
 removing <Marked_app(app(reverse2,app(app(cons,x),xs)),l),Marked_app(
                                                            app(reverse2,
                                                             xs),
                                                            app(app(cons,x),l))>
 [ {
      
     DP termination of:
     <Marked_app(app(app(compose,f),g),x) , Marked_app(g,app(f,x))>
<Marked_app(app(app(compose,f),g),x) , Marked_app(f,x)>
<Marked_app(app(reverse2,app(app(cons,x),xs)),l) , Marked_app(app(cons,x),l)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_app(app(app(compose,f),g),x) , Marked_app(g,app(f,x))>
<Marked_app(app(app(compose,f),g),x) , Marked_app(f,x)>
<Marked_app(app(reverse2,app(app(cons,x),xs)),l) , Marked_app(app(cons,x),l)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ app ] (X0,X1) = 1*X1 + 1*X0; 
 [ last ] () = 3; 
 [ reverse ] () = 1; 
 [ reverse2 ] () = 1; 
 [ hd ] () = 0; 
 [ compose ] () = 0; 
 [ init ] () = 3; 
 [ cons ] () = 2; 
 [ nil ] () = 0; 
 [ Marked_app ] (X0,X1) = 2*X1 + 3*X0; 
 [ tl ] () = 0; 
 removing <Marked_app(app(reverse2,app(app(cons,x),xs)),l),Marked_app(
                                                            app(cons,
                                                             x),l)>
 [ {
      
     DP termination of:
     <Marked_app(app(app(compose,f),g),x) , Marked_app(g,app(f,x))>
<Marked_app(app(app(compose,f),g),x) , Marked_app(f,x)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_app(app(app(compose,f),g),x) , Marked_app(g,app(f,x))>
<Marked_app(app(app(compose,f),g),x) , Marked_app(f,x)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ app ] (X0,X1) = 1*X0 + 1*X1 + 0; 
 [ last ] () = 3 + 0; 
 [ reverse ] () = 0; 
 [ reverse2 ] () = 0; 
 [ hd ] () = 0; 
 [ compose ] () = 1 + 0; 
 [ init ] () = 3 + 0; 
 [ cons ] () = 3 + 0; 
 [ nil ] () = 0; 
 [ Marked_app ] (X0,X1) = 3*X0 + 3*X1 + 0; 
 [ tl ] () = 0; 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 

Cime worked for 0.421093 seconds (real time)
Cime Exit Status: 0