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

TRS termination of:
[1] app(app(mapt,f),app(leaf,x)) -> app(leaf,app(f,x))
[2] app(app(mapt,f),app(node,xs)) -> app(node,app(app(maptlist,f),xs))
[3] app(app(maptlist,f),nil) -> nil
[4] app(app(maptlist,f),app(app(cons,x),xs)) ->
 app(app(cons,app(app(mapt,f),x)),app(app(maptlist,f),xs))


Sub problem: 
guided: 

DP termination of:
<Marked_app(app(mapt,f),app(leaf,x)) , Marked_app(leaf,app(f,x))>
<Marked_app(app(mapt,f),app(leaf,x)) , Marked_app(f,x)>
<Marked_app(app(mapt,f),app(node,xs)) , Marked_app(node,
                                         app(app(maptlist,f),xs))>
<Marked_app(app(mapt,f),app(node,xs)) , Marked_app(app(maptlist,f),xs)>
<Marked_app(app(mapt,f),app(node,xs)) , Marked_app(maptlist,f)>
<Marked_app(app(maptlist,f),app(app(cons,x),xs)) , Marked_app(app(cons,
                                                               app(app(mapt,f),
                                                                x)),
                                                    app(app(maptlist,f),xs))>
<Marked_app(app(maptlist,f),app(app(cons,x),xs)) , Marked_app(cons,
                                                    app(app(mapt,f),x))>
<Marked_app(app(maptlist,f),app(app(cons,x),xs)) , Marked_app(app(mapt,f),x)>
<Marked_app(app(maptlist,f),app(app(cons,x),xs)) , Marked_app(mapt,f)>
<Marked_app(app(maptlist,f),app(app(cons,x),xs)) , Marked_app(app(maptlist,f),
                                                    xs)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_app(app(maptlist,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                  maptlist,
                                                                  f),
                                                       xs)> 
      --> <Marked_app(app(maptlist,f),app(app(cons,x),xs)) , Marked_app(
                                                              app(maptlist,
                                                               f),xs)>
  <Marked_app(app(maptlist,f),app(app(cons,x),xs)) , Marked_app(app(maptlist,f),
                                                      xs)> 
     --> <Marked_app(app(maptlist,f),app(app(cons,x),xs)) , Marked_app(
                                                             app(mapt,
                                                              f),x)>
  <Marked_app(app(maptlist,f),app(app(cons,x),xs)) , Marked_app(app(maptlist,f),
                                                      xs)> 
     --> <Marked_app(app(maptlist,f),app(app(cons,x),xs)) , Marked_app(
                                                             app(cons,
                                                              app(app(mapt,f),
                                                               x)),
                                                             app(app(
                                                                  maptlist,
                                                                  f),
                                                              xs))>
  <Marked_app(app(maptlist,f),app(app(cons,x),xs)) , Marked_app(app(maptlist,f),
                                                      xs)> 
     --> <Marked_app(app(mapt,f),app(node,xs)) , Marked_app(app(maptlist,f),xs)>
  <Marked_app(app(maptlist,f),app(app(cons,x),xs)) , Marked_app(app(maptlist,f),
                                                      xs)> 
     --> <Marked_app(app(mapt,f),app(leaf,x)) , Marked_app(f,x)>
  <Marked_app(app(maptlist,f),app(app(cons,x),xs)) , Marked_app(app(mapt,f),x)> 
     --> <Marked_app(app(maptlist,f),app(app(cons,x),xs)) , Marked_app(
                                                             app(maptlist,
                                                              f),xs)>
  <Marked_app(app(maptlist,f),app(app(cons,x),xs)) , Marked_app(app(mapt,f),x)> 
     --> <Marked_app(app(maptlist,f),app(app(cons,x),xs)) , Marked_app(
                                                             app(mapt,
                                                              f),x)>
  <Marked_app(app(maptlist,f),app(app(cons,x),xs)) , Marked_app(app(mapt,f),x)> 
     --> <Marked_app(app(maptlist,f),app(app(cons,x),xs)) , Marked_app(
                                                             app(cons,
                                                              app(app(mapt,f),
                                                               x)),
                                                             app(app(
                                                                  maptlist,
                                                                  f),
                                                              xs))>
  <Marked_app(app(maptlist,f),app(app(cons,x),xs)) , Marked_app(app(mapt,f),x)> 
     --> <Marked_app(app(mapt,f),app(node,xs)) , Marked_app(app(maptlist,f),xs)>
  <Marked_app(app(maptlist,f),app(app(cons,x),xs)) , Marked_app(app(mapt,f),x)> 
     --> <Marked_app(app(mapt,f),app(leaf,x)) , Marked_app(f,x)>
  <Marked_app(app(maptlist,f),app(app(cons,x),xs)) , Marked_app(app(cons,
                                                                 app(
                                                                  app(
                                                                   mapt,
                                                                   f),
                                                                  x)),
                                                      app(app(maptlist,f),xs))> 
     --> <Marked_app(app(maptlist,f),app(app(cons,x),xs)) , Marked_app(
                                                             app(maptlist,
                                                              f),xs)>
  <Marked_app(app(maptlist,f),app(app(cons,x),xs)) , Marked_app(app(cons,
                                                                 app(
                                                                  app(
                                                                   mapt,
                                                                   f),
                                                                  x)),
                                                      app(app(maptlist,f),xs))> 
     --> <Marked_app(app(maptlist,f),app(app(cons,x),xs)) , Marked_app(
                                                             app(mapt,
                                                              f),x)>
  <Marked_app(app(maptlist,f),app(app(cons,x),xs)) , Marked_app(app(cons,
                                                                 app(
                                                                  app(
                                                                   mapt,
                                                                   f),
                                                                  x)),
                                                      app(app(maptlist,f),xs))> 
     --> <Marked_app(app(maptlist,f),app(app(cons,x),xs)) , Marked_app(
                                                             app(cons,
                                                              app(app(mapt,f),
                                                               x)),
                                                             app(app(
                                                                  maptlist,
                                                                  f),
                                                              xs))>
  <Marked_app(app(maptlist,f),app(app(cons,x),xs)) , Marked_app(app(cons,
                                                                 app(
                                                                  app(
                                                                   mapt,
                                                                   f),
                                                                  x)),
                                                      app(app(maptlist,f),xs))> 
     --> <Marked_app(app(mapt,f),app(node,xs)) , Marked_app(app(maptlist,f),xs)>
  <Marked_app(app(maptlist,f),app(app(cons,x),xs)) , Marked_app(app(cons,
                                                                 app(
                                                                  app(
                                                                   mapt,
                                                                   f),
                                                                  x)),
                                                      app(app(maptlist,f),xs))> 
     --> <Marked_app(app(mapt,f),app(leaf,x)) , Marked_app(f,x)>
  <Marked_app(app(mapt,f),app(node,xs)) , Marked_app(app(maptlist,f),xs)> 
     --> <Marked_app(app(maptlist,f),app(app(cons,x),xs)) , Marked_app(
                                                             app(maptlist,
                                                              f),xs)>
  <Marked_app(app(mapt,f),app(node,xs)) , Marked_app(app(maptlist,f),xs)> 
     --> <Marked_app(app(maptlist,f),app(app(cons,x),xs)) , Marked_app(
                                                             app(mapt,
                                                              f),x)>
  <Marked_app(app(mapt,f),app(node,xs)) , Marked_app(app(maptlist,f),xs)> 
     --> <Marked_app(app(maptlist,f),app(app(cons,x),xs)) , Marked_app(
                                                             app(cons,
                                                              app(app(mapt,f),
                                                               x)),
                                                             app(app(
                                                                  maptlist,
                                                                  f),
                                                              xs))>
  <Marked_app(app(mapt,f),app(node,xs)) , Marked_app(app(maptlist,f),xs)> 
     --> <Marked_app(app(mapt,f),app(node,xs)) , Marked_app(app(maptlist,f),xs)>
  <Marked_app(app(mapt,f),app(node,xs)) , Marked_app(app(maptlist,f),xs)> 
     --> <Marked_app(app(mapt,f),app(leaf,x)) , Marked_app(f,x)>
  <Marked_app(app(mapt,f),app(leaf,x)) , Marked_app(f,x)> 
     --> <Marked_app(app(maptlist,f),app(app(cons,x),xs)) , Marked_app(
                                                             app(maptlist,
                                                              f),xs)>
  <Marked_app(app(mapt,f),app(leaf,x)) , Marked_app(f,x)> 
     --> <Marked_app(app(maptlist,f),app(app(cons,x),xs)) , Marked_app(
                                                             app(mapt,
                                                              f),x)>
  <Marked_app(app(mapt,f),app(leaf,x)) , Marked_app(f,x)> 
     --> <Marked_app(app(maptlist,f),app(app(cons,x),xs)) , Marked_app(
                                                             app(cons,
                                                              app(app(mapt,f),
                                                               x)),
                                                             app(app(
                                                                  maptlist,
                                                                  f),
                                                              xs))>
  <Marked_app(app(mapt,f),app(leaf,x)) , Marked_app(f,x)> 
     --> <Marked_app(app(mapt,f),app(node,xs)) , Marked_app(app(maptlist,f),xs)>
  <Marked_app(app(mapt,f),app(leaf,x)) , Marked_app(f,x)> 
     --> <Marked_app(app(mapt,f),app(leaf,x)) , Marked_app(f,x)>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  app(app(mapt,f),app(leaf,x)) >= app(leaf,app(f,x)) ;
  app(app(mapt,f),app(node,xs)) >= app(node,app(app(maptlist,f),xs)) ;
  app(app(maptlist,f),app(app(cons,x),xs)) >= app(app(cons,app(app(mapt,f),x)),
                                               app(app(maptlist,f),xs)) ;
  app(app(maptlist,f),nil) >= nil ;
  Marked_app(app(mapt,f),app(leaf,x)) >= Marked_app(f,x) ;
  Marked_app(app(mapt,f),app(node,xs)) >= Marked_app(app(maptlist,f),xs) ;
  Marked_app(app(maptlist,f),app(app(cons,x),xs)) >= Marked_app(app(mapt,f),x) ;
  Marked_app(app(maptlist,f),app(app(cons,x),xs)) >= Marked_app(app(maptlist,f),
                                                      xs) ;
  Marked_app(app(maptlist,f),app(app(cons,x),xs)) >= Marked_app(app(cons,
                                                                 app(
                                                                  app(
                                                                   mapt,
                                                                   f),
                                                                  x)),
                                                      app(app(maptlist,f),xs)) ;
 }
 + Disjunctions:{ 
{
  Marked_app(app(mapt,f),app(leaf,x)) > Marked_app(f,x) ;
 }
{
  Marked_app(app(mapt,f),app(node,xs)) > Marked_app(app(maptlist,f),xs) ;
 }
{
  Marked_app(app(maptlist,f),app(app(cons,x),xs)) > Marked_app(app(mapt,f),x) ;
 }
{
  Marked_app(app(maptlist,f),app(app(cons,x),xs)) > Marked_app(app(maptlist,f),
                                                     xs) ;
 }
{
  Marked_app(app(maptlist,f),app(app(cons,x),xs)) > Marked_app(app(cons,
                                                                app(app(mapt,f),
                                                                 x)),
                                                     app(app(maptlist,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 : 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(mapt,f),app(leaf,x)) >= app(leaf,app(f,x))
constraint: app(app(mapt,f),app(node,xs)) >= app(node,app(app(maptlist,f),xs))
constraint: app(app(maptlist,f),app(app(cons,x),xs)) >= app(app(cons,
                                                             app(app(mapt,f),x)),
                                                         app(app(maptlist,f),
                                                          xs))
constraint: app(app(maptlist,f),nil) >= nil
constraint: Marked_app(app(mapt,f),app(leaf,x)) >= Marked_app(f,x)
constraint: Marked_app(app(mapt,f),app(node,xs)) >= Marked_app(app(maptlist,f),
                                                     xs)
constraint: Marked_app(app(maptlist,f),app(app(cons,x),xs)) >= Marked_app(
                                                                app(mapt,
                                                                 f),x)
constraint: Marked_app(app(maptlist,f),app(app(cons,x),xs)) >= Marked_app(
                                                                app(maptlist,
                                                                 f),xs)
constraint: Marked_app(app(maptlist,f),app(app(cons,x),xs)) >= Marked_app(
                                                                app(cons,
                                                                 app(
                                                                  app(
                                                                   mapt,
                                                                   f),
                                                                  x)),
                                                                app(app(
                                                                    maptlist,
                                                                    f),
                                                                 xs))
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_app(app(maptlist,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                  maptlist,
                                                                  f),
                                                       xs)> 
      --> <Marked_app(app(maptlist,f),app(app(cons,x),xs)) , Marked_app(
                                                              app(maptlist,
                                                               f),xs)>
  <Marked_app(app(maptlist,f),app(app(cons,x),xs)) , Marked_app(app(maptlist,f),
                                                      xs)> 
     --> <Marked_app(app(maptlist,f),app(app(cons,x),xs)) , Marked_app(
                                                             app(mapt,
                                                              f),x)>
  <Marked_app(app(maptlist,f),app(app(cons,x),xs)) , Marked_app(app(maptlist,f),
                                                      xs)> 
     --> <Marked_app(app(mapt,f),app(node,xs)) , Marked_app(app(maptlist,f),xs)>
  <Marked_app(app(maptlist,f),app(app(cons,x),xs)) , Marked_app(app(mapt,f),x)> 
     --> <Marked_app(app(maptlist,f),app(app(cons,x),xs)) , Marked_app(
                                                             app(maptlist,
                                                              f),xs)>
  <Marked_app(app(maptlist,f),app(app(cons,x),xs)) , Marked_app(app(mapt,f),x)> 
     --> <Marked_app(app(maptlist,f),app(app(cons,x),xs)) , Marked_app(
                                                             app(mapt,
                                                              f),x)>
  <Marked_app(app(maptlist,f),app(app(cons,x),xs)) , Marked_app(app(mapt,f),x)> 
     --> <Marked_app(app(mapt,f),app(node,xs)) , Marked_app(app(maptlist,f),xs)>
  <Marked_app(app(mapt,f),app(node,xs)) , Marked_app(app(maptlist,f),xs)> 
     --> <Marked_app(app(maptlist,f),app(app(cons,x),xs)) , Marked_app(
                                                             app(maptlist,
                                                              f),xs)>
  <Marked_app(app(mapt,f),app(node,xs)) , Marked_app(app(maptlist,f),xs)> 
     --> <Marked_app(app(maptlist,f),app(app(cons,x),xs)) , Marked_app(
                                                             app(mapt,
                                                              f),x)>
  <Marked_app(app(mapt,f),app(node,xs)) , Marked_app(app(maptlist,f),xs)> 
     --> <Marked_app(app(mapt,f),app(node,xs)) , Marked_app(app(maptlist,f),xs)>
}
APPLY CRITERIA (Subterm criterion)

ST: Marked_app -> 2

APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] app(app(mapt,f),app(leaf,x)) -> app(leaf,app(f,x))
[2] app(app(mapt,f),app(node,xs)) -> app(node,app(app(maptlist,f),xs))
[3] app(app(maptlist,f),nil) -> nil
[4] app(app(maptlist,f),app(app(cons,x),xs)) ->
 app(app(cons,app(app(mapt,f),x)),app(app(maptlist,f),xs))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_app(app(mapt,f),app(leaf,x)) , Marked_app(leaf,app(f,x))>
<Marked_app(app(mapt,f),app(leaf,x)) , Marked_app(f,x)>
<Marked_app(app(mapt,f),app(node,xs)) , Marked_app(node,
                                         app(app(maptlist,f),xs))>
<Marked_app(app(mapt,f),app(node,xs)) , Marked_app(app(maptlist,f),xs)>
<Marked_app(app(mapt,f),app(node,xs)) , Marked_app(maptlist,f)>
<Marked_app(app(maptlist,f),app(app(cons,x),xs)) , Marked_app(app(cons,
                                                               app(app(mapt,f),
                                                                x)),
                                                    app(app(maptlist,f),xs))>
<Marked_app(app(maptlist,f),app(app(cons,x),xs)) , Marked_app(cons,
                                                    app(app(mapt,f),x))>
<Marked_app(app(maptlist,f),app(app(cons,x),xs)) , Marked_app(app(mapt,f),x)>
<Marked_app(app(maptlist,f),app(app(cons,x),xs)) , Marked_app(mapt,f)>
<Marked_app(app(maptlist,f),app(app(cons,x),xs)) , Marked_app(app(maptlist,f),
                                                    xs)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_app(app(mapt,f),app(leaf,x)) , Marked_app(f,x)>
<Marked_app(app(mapt,f),app(node,xs)) , Marked_app(app(maptlist,f),xs)>
<Marked_app(app(maptlist,f),app(app(cons,x),xs)) , Marked_app(app(cons,
                                                               app(app(mapt,f),
                                                                x)),
                                                    app(app(maptlist,f),xs))>
<Marked_app(app(maptlist,f),app(app(cons,x),xs)) , Marked_app(app(mapt,f),x)>
<Marked_app(app(maptlist,f),app(app(cons,x),xs)) , Marked_app(app(maptlist,f),
                                                    xs)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ app ] (X0,X1) = 2*X1*X0 + 2*X0; 
 [ maptlist ] () = 2; 
 [ mapt ] () = 2; 
 [ cons ] () = 0; 
 [ leaf ] () = 0; 
 [ nil ] () = 1; 
 [ node ] () = 0; 
 [ Marked_app ] (X0,X1) = 2*X0; 
 removing <Marked_app(app(mapt,f),app(leaf,x)),Marked_app(f,x)><Marked_app(
                                                                 app(
                                                                  maptlist,
                                                                  f),
                                                                 app(
                                                                  app(
                                                                   cons,
                                                                   x),
                                                                  xs)),
Marked_app(app(cons,app(app(mapt,f),x)),app(app(maptlist,f),xs))>
 [ {
      
     DP termination of:
     <Marked_app(app(mapt,f),app(node,xs)) , Marked_app(app(maptlist,f),xs)>
<Marked_app(app(maptlist,f),app(app(cons,x),xs)) , Marked_app(app(mapt,f),x)>
<Marked_app(app(maptlist,f),app(app(cons,x),xs)) , Marked_app(app(maptlist,f),
                                                    xs)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_app(app(mapt,f),app(node,xs)) , Marked_app(app(maptlist,f),xs)>
<Marked_app(app(maptlist,f),app(app(cons,x),xs)) , Marked_app(app(mapt,f),x)>
<Marked_app(app(maptlist,f),app(app(cons,x),xs)) , Marked_app(app(maptlist,f),
                                                    xs)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 
 ]} 
 ]} 

Cime worked for 3.257300 seconds (real time)
Cime Exit Status: 0