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

TRS termination of:
[1] app(id,x) -> x
[2] app(add,0) -> id
[3] app(app(add,app(s,x)),y) -> app(s,app(app(add,x),y))
[4] app(app(map,f),nil) -> nil
[5] app(app(map,f),app(app(cons,x),xs)) ->
 app(app(cons,app(f,x)),app(app(map,f),xs))


Sub problem: 
guided: 

DP termination of:
<Marked_app(app(add,app(s,x)),y) , Marked_app(s,app(app(add,x),y))>
<Marked_app(app(add,app(s,x)),y) , Marked_app(app(add,x),y)>
<Marked_app(app(add,app(s,x)),y) , Marked_app(add,x)>
<Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(cons,app(f,x)),
                                               app(app(map,f),xs))>
<Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(cons,app(f,x))>
<Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)>
<Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),xs)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),xs)> 
      --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),
                                                         xs)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),xs)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),xs)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                   cons,
                                                                   app(f,x)),
                                                        app(app(map,f),xs))>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),xs)> 
     --> <Marked_app(app(add,app(s,x)),y) , Marked_app(app(add,x),y)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),
                                                        xs)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                   cons,
                                                                   app(f,x)),
                                                        app(app(map,f),xs))>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)> 
     --> <Marked_app(app(add,app(s,x)),y) , Marked_app(app(add,x),y)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(cons,app(f,x)),
                                                 app(app(map,f),xs))> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),
                                                        xs)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(cons,app(f,x)),
                                                 app(app(map,f),xs))> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(cons,app(f,x)),
                                                 app(app(map,f),xs))> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                   cons,
                                                                   app(f,x)),
                                                        app(app(map,f),xs))>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(cons,app(f,x)),
                                                 app(app(map,f),xs))> 
     --> <Marked_app(app(add,app(s,x)),y) , Marked_app(app(add,x),y)>
  <Marked_app(app(add,app(s,x)),y) , Marked_app(app(add,x),y)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),
                                                        xs)>
  <Marked_app(app(add,app(s,x)),y) , Marked_app(app(add,x),y)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)>
  <Marked_app(app(add,app(s,x)),y) , Marked_app(app(add,x),y)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                   cons,
                                                                   app(f,x)),
                                                        app(app(map,f),xs))>
  <Marked_app(app(add,app(s,x)),y) , Marked_app(app(add,x),y)> 
     --> <Marked_app(app(add,app(s,x)),y) , Marked_app(app(add,x),y)>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  app(app(add,app(s,x)),y) >= app(s,app(app(add,x),y)) ;
  app(app(map,f),app(app(cons,x),xs)) >= app(app(cons,app(f,x)),
                                          app(app(map,f),xs)) ;
  app(app(map,f),nil) >= nil ;
  app(id,x) >= x ;
  app(add,0) >= id ;
  Marked_app(app(add,app(s,x)),y) >= Marked_app(app(add,x),y) ;
  Marked_app(app(map,f),app(app(cons,x),xs)) >= Marked_app(app(map,f),xs) ;
  Marked_app(app(map,f),app(app(cons,x),xs)) >= Marked_app(app(cons,app(f,x)),
                                                 app(app(map,f),xs)) ;
  Marked_app(app(map,f),app(app(cons,x),xs)) >= Marked_app(f,x) ;
 }
 + Disjunctions:{ 
{
  Marked_app(app(add,app(s,x)),y) > Marked_app(app(add,x),y) ;
 }
{
  Marked_app(app(map,f),app(app(cons,x),xs)) > Marked_app(app(map,f),xs) ;
 }
{
  Marked_app(app(map,f),app(app(cons,x),xs)) > Marked_app(app(cons,app(f,x)),
                                                app(app(map,f),xs)) ;
 }
{
  Marked_app(app(map,f),app(app(cons,x),xs)) > Marked_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
=== 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 : 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(add,app(s,x)),y) >= app(s,app(app(add,x),y))
constraint: app(app(map,f),app(app(cons,x),xs)) >= app(app(cons,app(f,x)),
                                                    app(app(map,f),xs))
constraint: app(app(map,f),nil) >= nil
constraint: app(id,x) >= x
constraint: app(add,0) >= id
constraint: Marked_app(app(add,app(s,x)),y) >= Marked_app(app(add,x),y)
constraint: Marked_app(app(map,f),app(app(cons,x),xs)) >= Marked_app(
                                                           app(map,f),
                                                           xs)
constraint: Marked_app(app(map,f),app(app(cons,x),xs)) >= Marked_app(
                                                           app(cons,app(f,x)),
                                                           app(app(map,f),xs))
constraint: Marked_app(app(map,f),app(app(cons,x),xs)) >= Marked_app(f,x)
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),xs)> 
      --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),
                                                         xs)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),xs)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                   cons,
                                                                   app(f,x)),
                                                        app(app(map,f),xs))>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),xs)> 
     --> <Marked_app(app(add,app(s,x)),y) , Marked_app(app(add,x),y)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(cons,app(f,x)),
                                                 app(app(map,f),xs))> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),
                                                        xs)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(cons,app(f,x)),
                                                 app(app(map,f),xs))> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                   cons,
                                                                   app(f,x)),
                                                        app(app(map,f),xs))>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(cons,app(f,x)),
                                                 app(app(map,f),xs))> 
     --> <Marked_app(app(add,app(s,x)),y) , Marked_app(app(add,x),y)>
  <Marked_app(app(add,app(s,x)),y) , Marked_app(app(add,x),y)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),
                                                        xs)>
  <Marked_app(app(add,app(s,x)),y) , Marked_app(app(add,x),y)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                   cons,
                                                                   app(f,x)),
                                                        app(app(map,f),xs))>
  <Marked_app(app(add,app(s,x)),y) , Marked_app(app(add,x),y)> 
     --> <Marked_app(app(add,app(s,x)),y) , Marked_app(app(add,x),y)>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  app(app(add,app(s,x)),y) >= app(s,app(app(add,x),y)) ;
  app(app(map,f),app(app(cons,x),xs)) >= app(app(cons,app(f,x)),
                                          app(app(map,f),xs)) ;
  app(app(map,f),nil) >= nil ;
  app(id,x) >= x ;
  app(add,0) >= id ;
  Marked_app(app(add,app(s,x)),y) >= Marked_app(app(add,x),y) ;
  Marked_app(app(map,f),app(app(cons,x),xs)) >= Marked_app(app(map,f),xs) ;
  Marked_app(app(map,f),app(app(cons,x),xs)) >= Marked_app(app(cons,app(f,x)),
                                                 app(app(map,f),xs)) ;
 }
 + Disjunctions:{ 
{
  Marked_app(app(add,app(s,x)),y) > Marked_app(app(add,x),y) ;
 }
{
  Marked_app(app(map,f),app(app(cons,x),xs)) > Marked_app(app(map,f),xs) ;
 }
{
  Marked_app(app(map,f),app(app(cons,x),xs)) > Marked_app(app(cons,app(f,x)),
                                                app(app(map,f),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
=== 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 : 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(add,app(s,x)),y) >= app(s,app(app(add,x),y))
constraint: app(app(map,f),app(app(cons,x),xs)) >= app(app(cons,app(f,x)),
                                                    app(app(map,f),xs))
constraint: app(app(map,f),nil) >= nil
constraint: app(id,x) >= x
constraint: app(add,0) >= id
constraint: Marked_app(app(add,app(s,x)),y) >= Marked_app(app(add,x),y)
constraint: Marked_app(app(map,f),app(app(cons,x),xs)) >= Marked_app(
                                                           app(map,f),
                                                           xs)
constraint: Marked_app(app(map,f),app(app(cons,x),xs)) >= Marked_app(
                                                           app(cons,app(f,x)),
                                                           app(app(map,f),xs))
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(cons,app(f,x)),
                                                  app(app(map,f),xs))> 
      --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                    cons,
                                                                    app(f,x)),
                                                         app(app(map,f),xs))>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(cons,app(f,x)),
                                                 app(app(map,f),xs))> 
     --> <Marked_app(app(add,app(s,x)),y) , Marked_app(app(add,x),y)>
  <Marked_app(app(add,app(s,x)),y) , Marked_app(app(add,x),y)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                   cons,
                                                                   app(f,x)),
                                                        app(app(map,f),xs))>
  <Marked_app(app(add,app(s,x)),y) , Marked_app(app(add,x),y)> 
     --> <Marked_app(app(add,app(s,x)),y) , Marked_app(app(add,x),y)>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  app(app(add,app(s,x)),y) >= app(s,app(app(add,x),y)) ;
  app(app(map,f),app(app(cons,x),xs)) >= app(app(cons,app(f,x)),
                                          app(app(map,f),xs)) ;
  app(app(map,f),nil) >= nil ;
  app(id,x) >= x ;
  app(add,0) >= id ;
  Marked_app(app(add,app(s,x)),y) >= Marked_app(app(add,x),y) ;
  Marked_app(app(map,f),app(app(cons,x),xs)) >= Marked_app(app(cons,app(f,x)),
                                                 app(app(map,f),xs)) ;
 }
 + Disjunctions:{ 
{
  Marked_app(app(add,app(s,x)),y) > Marked_app(app(add,x),y) ;
 }
{
  Marked_app(app(map,f),app(app(cons,x),xs)) > Marked_app(app(cons,app(f,x)),
                                                app(app(map,f),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
=== 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 : 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(add,app(s,x)),y) >= app(s,app(app(add,x),y))
constraint: app(app(map,f),app(app(cons,x),xs)) >= app(app(cons,app(f,x)),
                                                    app(app(map,f),xs))
constraint: app(app(map,f),nil) >= nil
constraint: app(id,x) >= x
constraint: app(add,0) >= id
constraint: Marked_app(app(add,app(s,x)),y) >= Marked_app(app(add,x),y)
constraint: Marked_app(app(map,f),app(app(cons,x),xs)) >= Marked_app(
                                                           app(cons,app(f,x)),
                                                           app(app(map,f),xs))
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(cons,app(f,x)),
                                                  app(app(map,f),xs))> 
      --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                    cons,
                                                                    app(f,x)),
                                                         app(app(map,f),xs))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  app(app(add,app(s,x)),y) >= app(s,app(app(add,x),y)) ;
  app(app(map,f),app(app(cons,x),xs)) >= app(app(cons,app(f,x)),
                                          app(app(map,f),xs)) ;
  app(app(map,f),nil) >= nil ;
  app(id,x) >= x ;
  app(add,0) >= id ;
  Marked_app(app(map,f),app(app(cons,x),xs)) >= Marked_app(app(cons,app(f,x)),
                                                 app(app(map,f),xs)) ;
 }
 + Disjunctions:{ 
{
  Marked_app(app(map,f),app(app(cons,x),xs)) > Marked_app(app(cons,app(f,x)),
                                                app(app(map,f),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
=== 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 : 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(add,app(s,x)),y) >= app(s,app(app(add,x),y))
constraint: app(app(map,f),app(app(cons,x),xs)) >= app(app(cons,app(f,x)),
                                                    app(app(map,f),xs))
constraint: app(app(map,f),nil) >= nil
constraint: app(id,x) >= x
constraint: app(add,0) >= id
constraint: Marked_app(app(map,f),app(app(cons,x),xs)) >= Marked_app(
                                                           app(cons,app(f,x)),
                                                           app(app(map,f),xs))
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] app(id,x) -> x
[2] app(add,0) -> id
[3] app(app(add,app(s,x)),y) -> app(s,app(app(add,x),y))
[4] app(app(map,f),nil) -> nil
[5] app(app(map,f),app(app(cons,x),xs)) ->
 app(app(cons,app(f,x)),app(app(map,f),xs))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_app(app(add,app(s,x)),y) , Marked_app(s,app(app(add,x),y))>
<Marked_app(app(add,app(s,x)),y) , Marked_app(app(add,x),y)>
<Marked_app(app(add,app(s,x)),y) , Marked_app(add,x)>
<Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(cons,app(f,x)),
                                               app(app(map,f),xs))>
<Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(cons,app(f,x))>
<Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)>
<Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),xs)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_app(app(add,app(s,x)),y) , Marked_app(app(add,x),y)>
<Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(cons,app(f,x)),
                                               app(app(map,f),xs))>
<Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)>
<Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),xs)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ app ] (X0,X1) = 2*X1*X0 + 1; 
 [ Marked_app ] (X0,X1) = 1*X0; 
 [ s ] () = 0; 
 [ add ] () = 0; 
 [ map ] () = 2; 
 [ id ] () = 1; 
 [ nil ] () = 0; 
 [ 0 ] () = 0; 
 [ cons ] () = 0; 
 removing <Marked_app(app(map,f),app(app(cons,x),xs)),Marked_app(f,x)>
 [ {
      
     DP termination of:
     <Marked_app(app(add,app(s,x)),y) , Marked_app(app(add,x),y)>
<Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(cons,app(f,x)),
                                               app(app(map,f),xs))>
<Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),xs)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_app(app(add,app(s,x)),y) , Marked_app(app(add,x),y)>
<Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(cons,app(f,x)),
                                               app(app(map,f),xs))>
<Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),xs)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ app ] (X0,X1) = 2*X1*X0 + 1; 
 [ Marked_app ] (X0,X1) = 1*X1; 
 [ s ] () = 0; 
 [ add ] () = 0; 
 [ map ] () = 0; 
 [ id ] () = 1; 
 [ nil ] () = 0; 
 [ 0 ] () = 0; 
 [ cons ] () = 0; 
 removing <Marked_app(app(map,f),app(app(cons,x),xs)),Marked_app(app(map,f),xs)>
 [ {
      
     DP termination of:
     <Marked_app(app(add,app(s,x)),y) , Marked_app(app(add,x),y)>
<Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(cons,app(f,x)),
                                               app(app(map,f),xs))>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_app(app(add,app(s,x)),y) , Marked_app(app(add,x),y)>
<Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(cons,app(f,x)),
                                               app(app(map,f),xs))>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ app ] (X0,X1) = 2*X1*X0 + 2*X0; 
 [ Marked_app ] (X0,X1) = 2*X0; 
 [ s ] () = 2; 
 [ add ] () = 1; 
 [ map ] () = 0; 
 [ id ] () = 1; 
 [ nil ] () = 0; 
 [ 0 ] () = 1; 
 [ cons ] () = 0; 
 removing <Marked_app(app(add,app(s,x)),y),Marked_app(app(add,x),y)>
 [ {
      
     DP termination of:
     <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(cons,
                                                               app(f,x)),
                                                    app(app(map,f),xs))>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(cons,
                                                               app(f,x)),
                                                    app(app(map,f),xs))>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ app ] (X0,X1) = 2*X0 + 2*X1*X0 + 0; 
 [ Marked_app ] (X0,X1) = 1*X0 + 0; 
 [ s ] () = 1 + 0; 
 [ add ] () = 1 + 0; 
 [ map ] () = 1 + 0; 
 [ id ] () = 1 + 0; 
 [ nil ] () = 0; 
 [ 0 ] () = 0; 
 [ cons ] () = 0; 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 

Cime worked for 5.569836 seconds (real time)
Cime Exit Status: 0