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

TRS termination of:
[1] app(app(minus,0),y) -> 0
[2] app(app(minus,app(s,x)),0) -> app(s,x)
[3] app(app(minus,app(s,x)),app(s,y)) -> app(app(minus,x),y)
[4] app(app(le,0),y) -> true
[5] app(app(le,app(s,x)),0) -> false
[6] app(app(le,app(s,x)),app(s,y)) -> app(app(le,x),y)
[7] app(app(app(if,true),x),y) -> x
[8] app(app(app(if,false),x),y) -> y
[9] app(perfectp,0) -> false
[10] app(perfectp,app(s,x)) ->
 app(app(app(app(f,x),app(s,0)),app(s,x)),app(s,x))
[11] app(app(app(app(f,0),y),0),u) -> true
[12] app(app(app(app(f,0),y),app(s,z)),u) -> false
[13] app(app(app(app(f,app(s,x)),0),z),u) ->
 app(app(app(app(f,x),u),app(app(minus,z),app(s,x))),u)
[14] app(app(app(app(f,app(s,x)),app(s,y)),z),u) ->
 app(app(app(if,app(app(le,x),y)),
      app(app(app(app(f,app(s,x)),app(app(minus,y),x)),z),u)),
  app(app(app(app(f,x),u),z),u))
[15] app(app(map,fun),nil) -> nil
[16] app(app(map,fun),app(app(cons,x),xs)) ->
 app(app(cons,app(fun,x)),app(app(map,fun),xs))
[17] app(app(filter,fun),nil) -> nil
[18] app(app(filter,fun),app(app(cons,x),xs)) ->
 app(app(app(app(filter2,app(fun,x)),fun),x),xs)
[19] app(app(app(app(filter2,true),fun),x),xs) ->
 app(app(cons,x),app(app(filter,fun),xs))
[20] app(app(app(app(filter2,false),fun),x),xs) -> app(app(filter,fun),xs)


Sub problem: 
guided: 

DP termination of:
<Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)>
<Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(minus,x)>
<Marked_app(app(le,app(s,x)),app(s,y)) , Marked_app(app(le,x),y)>
<Marked_app(app(le,app(s,x)),app(s,y)) , Marked_app(le,x)>
<Marked_app(perfectp,app(s,x)) , Marked_app(app(app(app(f,x),app(s,0)),
                                             app(s,x)),app(s,x))>
<Marked_app(perfectp,app(s,x)) , Marked_app(app(app(f,x),app(s,0)),app(s,x))>
<Marked_app(perfectp,app(s,x)) , Marked_app(app(f,x),app(s,0))>
<Marked_app(perfectp,app(s,x)) , Marked_app(f,x)>
<Marked_app(perfectp,app(s,x)) , Marked_app(s,0)>
<Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(app(app(f,x),u),
                                                           app(app(minus,z),
                                                            app(s,x))),
                                                u)>
<Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(app(f,x),u),
                                                app(app(minus,z),app(s,x)))>
<Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(f,x),u)>
<Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(f,x)>
<Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(minus,z),
                                                app(s,x))>
<Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(minus,z)>
<Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                  app(
                                                                   if,
                                                                   app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                                  app(
                                                                   app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                                   u)),
                                                       app(app(app(app(f,x),u),
                                                            z),u))>
<Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                  if,
                                                                  app(
                                                                   app(le,x),
                                                                   y)),
                                                       app(app(app(app(
                                                                    f,
                                                                    app(s,x)),
                                                                app(app(
                                                                    minus,
                                                                    y),
                                                                 x)),
                                                            z),u))>
<Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(if,
                                                       app(app(le,x),y))>
<Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(le,x),y)>
<Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(le,x)>
<Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                  app(
                                                                   app(
                                                                    f,
                                                                    app(s,x)),
                                                                   app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                  z),
                                                       u)>
<Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                  app(
                                                                   f,
                                                                   app(s,x)),
                                                                  app(
                                                                   app(
                                                                    minus,
                                                                    y),
                                                                   x)),
                                                       z)>
<Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                  f,app(s,x)),
                                                       app(app(minus,y),x))>
<Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(minus,y),
                                                       x)>
<Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(minus,y)>
<Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                  app(
                                                                   app(f,x),
                                                                   u),
                                                                  z),
                                                       u)>
<Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                  app(f,x),
                                                                  u),
                                                       z)>
<Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(f,x),u)>
<Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(f,x)>
<Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(cons,app(fun,x)),
                                                 app(app(map,fun),xs))>
<Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(cons,app(fun,x))>
<Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
<Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(map,fun),xs)>
<Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                   app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                   fun),
                                                               x),xs)>
<Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                   filter2,
                                                                   app(fun,x)),
                                                               fun),x)>
<Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(filter2,
                                                               app(fun,x)),
                                                    fun)>
<Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(filter2,
                                                    app(fun,x))>
<Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
<Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(cons,x),
                                                     app(app(filter,fun),xs))>
<Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(cons,x)>
<Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(filter,fun),
                                                     xs)>
<Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(filter,fun)>
<Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(app(filter,fun),
                                                      xs)>
<Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(filter,fun)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(app(
                                                                    filter,
                                                                    fun),
                                                         xs)> 
      --> <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(
                                                                app(filter,
                                                                 fun),
                                                                xs)>
  <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(app(
                                                                   filter,
                                                                   fun),
                                                        xs)> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(filter,
                                                               fun),xs)>
  <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(app(
                                                                   filter,
                                                                   fun),
                                                        xs)> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(cons,
                                                               x),
                                                              app(app(
                                                                   filter,
                                                                   fun),
                                                               xs))>
  <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(app(
                                                                   filter,
                                                                   fun),
                                                        xs)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(app(
                                                                   filter,
                                                                   fun),
                                                        xs)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(filter2,
                                                              app(fun,x)),
                                                             fun)>
  <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(app(
                                                                   filter,
                                                                   fun),
                                                        xs)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  filter2,
                                                                  app(fun,x)),
                                                              fun),x)>
  <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(app(
                                                                   filter,
                                                                   fun),
                                                        xs)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  app(
                                                                   filter2,
                                                                   app(fun,x)),
                                                                  fun),
                                                              x),xs)>
  <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(app(
                                                                   filter,
                                                                   fun),
                                                        xs)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    map,
                                                                    fun),
                                                          xs)>
  <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(app(
                                                                   filter,
                                                                   fun),
                                                        xs)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(app(
                                                                   filter,
                                                                   fun),
                                                        xs)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    cons,
                                                                    app(fun,x)),
                                                          app(app(map,fun),xs))>
  <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(app(
                                                                   filter,
                                                                   fun),
                                                        xs)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(f,
                                                                 x),u)>
  <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(app(
                                                                   filter,
                                                                   fun),
                                                        xs)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(f,x),
                                                                 u),z)>
  <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(app(
                                                                   filter,
                                                                   fun),
                                                        xs)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                 z),u)>
  <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(app(
                                                                   filter,
                                                                   fun),
                                                        xs)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(minus,
                                                                 y),x)>
  <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(app(
                                                                   filter,
                                                                   fun),
                                                        xs)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(f,
                                                                 app(s,x)),
                                                                app(app(
                                                                    minus,
                                                                    y),
                                                                 x))>
  <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(app(
                                                                   filter,
                                                                   fun),
                                                        xs)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    f,
                                                                    app(s,x)),
                                                                 app(
                                                                  app(
                                                                   minus,
                                                                   y),
                                                                  x)),
                                                                z)>
  <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(app(
                                                                   filter,
                                                                   fun),
                                                        xs)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                 z),u)>
  <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(app(
                                                                   filter,
                                                                   fun),
                                                        xs)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(le,
                                                                 x),y)>
  <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(app(
                                                                   filter,
                                                                   fun),
                                                        xs)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(if,
                                                                 app(
                                                                  app(le,x),
                                                                  y)),
                                                                app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                                 u))>
  <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(app(
                                                                   filter,
                                                                   fun),
                                                        xs)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                                 app(
                                                                  app(
                                                                   app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                   z),
                                                                  u)),
                                                                app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    z),
                                                                 u))>
  <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(app(
                                                                   filter,
                                                                   fun),
                                                        xs)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(minus,z),
                                                         app(s,x))>
  <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(app(
                                                                   filter,
                                                                   fun),
                                                        xs)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(f,x),u)>
  <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(app(
                                                                   filter,
                                                                   fun),
                                                        xs)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(
                                                                    app(f,x),
                                                                    u),
                                                         app(app(minus,z),
                                                          app(s,x)))>
  <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(app(
                                                                   filter,
                                                                   fun),
                                                        xs)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    z),
                                                                    app(s,x))),
                                                         u)>
  <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(app(
                                                                   filter,
                                                                   fun),
                                                        xs)> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(f,x),app(s,0))>
  <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(app(
                                                                   filter,
                                                                   fun),
                                                        xs)> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(f,x),app(s,0)),
                                           app(s,x))>
  <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(app(
                                                                   filter,
                                                                   fun),
                                                        xs)> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(app(f,x),app(s,0)),
                                                      app(s,x)),app(s,x))>
  <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(app(
                                                                   filter,
                                                                   fun),
                                                        xs)> 
     --> <Marked_app(app(le,app(s,x)),app(s,y)) , Marked_app(app(le,x),y)>
  <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(app(
                                                                   filter,
                                                                   fun),
                                                        xs)> 
     --> <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(
                                                                  filter,
                                                                  fun),
                                                       xs)> 
     --> <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(
                                                               app(filter,
                                                                fun),
                                                               xs)>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(
                                                                  filter,
                                                                  fun),
                                                       xs)> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(filter,
                                                               fun),xs)>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(
                                                                  filter,
                                                                  fun),
                                                       xs)> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(cons,
                                                               x),
                                                              app(app(
                                                                   filter,
                                                                   fun),
                                                               xs))>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(
                                                                  filter,
                                                                  fun),
                                                       xs)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(
                                                                  filter,
                                                                  fun),
                                                       xs)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(filter2,
                                                              app(fun,x)),
                                                             fun)>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(
                                                                  filter,
                                                                  fun),
                                                       xs)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  filter2,
                                                                  app(fun,x)),
                                                              fun),x)>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(
                                                                  filter,
                                                                  fun),
                                                       xs)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  app(
                                                                   filter2,
                                                                   app(fun,x)),
                                                                  fun),
                                                              x),xs)>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(
                                                                  filter,
                                                                  fun),
                                                       xs)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    map,
                                                                    fun),
                                                          xs)>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(
                                                                  filter,
                                                                  fun),
                                                       xs)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(
                                                                  filter,
                                                                  fun),
                                                       xs)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    cons,
                                                                    app(fun,x)),
                                                          app(app(map,fun),xs))>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(
                                                                  filter,
                                                                  fun),
                                                       xs)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(f,
                                                                 x),u)>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(
                                                                  filter,
                                                                  fun),
                                                       xs)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(f,x),
                                                                 u),z)>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(
                                                                  filter,
                                                                  fun),
                                                       xs)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                 z),u)>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(
                                                                  filter,
                                                                  fun),
                                                       xs)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(minus,
                                                                 y),x)>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(
                                                                  filter,
                                                                  fun),
                                                       xs)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(f,
                                                                 app(s,x)),
                                                                app(app(
                                                                    minus,
                                                                    y),
                                                                 x))>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(
                                                                  filter,
                                                                  fun),
                                                       xs)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    f,
                                                                    app(s,x)),
                                                                 app(
                                                                  app(
                                                                   minus,
                                                                   y),
                                                                  x)),
                                                                z)>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(
                                                                  filter,
                                                                  fun),
                                                       xs)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                 z),u)>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(
                                                                  filter,
                                                                  fun),
                                                       xs)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(le,
                                                                 x),y)>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(
                                                                  filter,
                                                                  fun),
                                                       xs)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(if,
                                                                 app(
                                                                  app(le,x),
                                                                  y)),
                                                                app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                                 u))>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(
                                                                  filter,
                                                                  fun),
                                                       xs)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                                 app(
                                                                  app(
                                                                   app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                   z),
                                                                  u)),
                                                                app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    z),
                                                                 u))>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(
                                                                  filter,
                                                                  fun),
                                                       xs)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(minus,z),
                                                         app(s,x))>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(
                                                                  filter,
                                                                  fun),
                                                       xs)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(f,x),u)>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(
                                                                  filter,
                                                                  fun),
                                                       xs)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(
                                                                    app(f,x),
                                                                    u),
                                                         app(app(minus,z),
                                                          app(s,x)))>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(
                                                                  filter,
                                                                  fun),
                                                       xs)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    z),
                                                                    app(s,x))),
                                                         u)>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(
                                                                  filter,
                                                                  fun),
                                                       xs)> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(f,x),app(s,0))>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(
                                                                  filter,
                                                                  fun),
                                                       xs)> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(f,x),app(s,0)),
                                           app(s,x))>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(
                                                                  filter,
                                                                  fun),
                                                       xs)> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(app(f,x),app(s,0)),
                                                      app(s,x)),app(s,x))>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(
                                                                  filter,
                                                                  fun),
                                                       xs)> 
     --> <Marked_app(app(le,app(s,x)),app(s,y)) , Marked_app(app(le,x),y)>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(
                                                                  filter,
                                                                  fun),
                                                       xs)> 
     --> <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(cons,x),
                                                       app(app(filter,fun),xs))> 
     --> <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(
                                                               app(filter,
                                                                fun),
                                                               xs)>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(cons,x),
                                                       app(app(filter,fun),xs))> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(filter,
                                                               fun),xs)>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(cons,x),
                                                       app(app(filter,fun),xs))> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(cons,
                                                               x),
                                                              app(app(
                                                                   filter,
                                                                   fun),
                                                               xs))>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(cons,x),
                                                       app(app(filter,fun),xs))> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(cons,x),
                                                       app(app(filter,fun),xs))> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(filter2,
                                                              app(fun,x)),
                                                             fun)>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(cons,x),
                                                       app(app(filter,fun),xs))> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  filter2,
                                                                  app(fun,x)),
                                                              fun),x)>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(cons,x),
                                                       app(app(filter,fun),xs))> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  app(
                                                                   filter2,
                                                                   app(fun,x)),
                                                                  fun),
                                                              x),xs)>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(cons,x),
                                                       app(app(filter,fun),xs))> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    map,
                                                                    fun),
                                                          xs)>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(cons,x),
                                                       app(app(filter,fun),xs))> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(cons,x),
                                                       app(app(filter,fun),xs))> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    cons,
                                                                    app(fun,x)),
                                                          app(app(map,fun),xs))>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(cons,x),
                                                       app(app(filter,fun),xs))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(f,
                                                                 x),u)>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(cons,x),
                                                       app(app(filter,fun),xs))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(f,x),
                                                                 u),z)>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(cons,x),
                                                       app(app(filter,fun),xs))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                 z),u)>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(cons,x),
                                                       app(app(filter,fun),xs))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(minus,
                                                                 y),x)>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(cons,x),
                                                       app(app(filter,fun),xs))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(f,
                                                                 app(s,x)),
                                                                app(app(
                                                                    minus,
                                                                    y),
                                                                 x))>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(cons,x),
                                                       app(app(filter,fun),xs))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    f,
                                                                    app(s,x)),
                                                                 app(
                                                                  app(
                                                                   minus,
                                                                   y),
                                                                  x)),
                                                                z)>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(cons,x),
                                                       app(app(filter,fun),xs))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                 z),u)>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(cons,x),
                                                       app(app(filter,fun),xs))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(le,
                                                                 x),y)>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(cons,x),
                                                       app(app(filter,fun),xs))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(if,
                                                                 app(
                                                                  app(le,x),
                                                                  y)),
                                                                app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                                 u))>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(cons,x),
                                                       app(app(filter,fun),xs))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                                 app(
                                                                  app(
                                                                   app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                   z),
                                                                  u)),
                                                                app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    z),
                                                                 u))>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(cons,x),
                                                       app(app(filter,fun),xs))> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(minus,z),
                                                         app(s,x))>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(cons,x),
                                                       app(app(filter,fun),xs))> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(f,x),u)>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(cons,x),
                                                       app(app(filter,fun),xs))> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(
                                                                    app(f,x),
                                                                    u),
                                                         app(app(minus,z),
                                                          app(s,x)))>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(cons,x),
                                                       app(app(filter,fun),xs))> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    z),
                                                                    app(s,x))),
                                                         u)>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(cons,x),
                                                       app(app(filter,fun),xs))> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(f,x),app(s,0))>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(cons,x),
                                                       app(app(filter,fun),xs))> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(f,x),app(s,0)),
                                           app(s,x))>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(cons,x),
                                                       app(app(filter,fun),xs))> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(app(f,x),app(s,0)),
                                                      app(s,x)),app(s,x))>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(cons,x),
                                                       app(app(filter,fun),xs))> 
     --> <Marked_app(app(le,app(s,x)),app(s,y)) , Marked_app(app(le,x),y)>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(cons,x),
                                                       app(app(filter,fun),xs))> 
     --> <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(
                                                               app(filter,
                                                                fun),
                                                               xs)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(filter,
                                                               fun),xs)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(cons,
                                                               x),
                                                              app(app(
                                                                   filter,
                                                                   fun),
                                                               xs))>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(filter2,
                                                              app(fun,x)),
                                                             fun)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  filter2,
                                                                  app(fun,x)),
                                                              fun),x)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  app(
                                                                   filter2,
                                                                   app(fun,x)),
                                                                  fun),
                                                              x),xs)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    map,
                                                                    fun),
                                                          xs)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    cons,
                                                                    app(fun,x)),
                                                          app(app(map,fun),xs))>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(f,
                                                                 x),u)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(f,x),
                                                                 u),z)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                 z),u)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(minus,
                                                                 y),x)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(f,
                                                                 app(s,x)),
                                                                app(app(
                                                                    minus,
                                                                    y),
                                                                 x))>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    f,
                                                                    app(s,x)),
                                                                 app(
                                                                  app(
                                                                   minus,
                                                                   y),
                                                                  x)),
                                                                z)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                 z),u)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(le,
                                                                 x),y)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(if,
                                                                 app(
                                                                  app(le,x),
                                                                  y)),
                                                                app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                                 u))>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                                 app(
                                                                  app(
                                                                   app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                   z),
                                                                  u)),
                                                                app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    z),
                                                                 u))>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(minus,z),
                                                         app(s,x))>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(f,x),u)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(
                                                                    app(f,x),
                                                                    u),
                                                         app(app(minus,z),
                                                          app(s,x)))>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    z),
                                                                    app(s,x))),
                                                         u)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(f,x),app(s,0))>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(f,x),app(s,0)),
                                           app(s,x))>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(app(f,x),app(s,0)),
                                                      app(s,x)),app(s,x))>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(le,app(s,x)),app(s,y)) , Marked_app(app(le,x),y)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(filter2,
                                                                 app(fun,x)),
                                                      fun)> 
     --> <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(
                                                               app(filter,
                                                                fun),
                                                               xs)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(filter2,
                                                                 app(fun,x)),
                                                      fun)> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(filter,
                                                               fun),xs)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(filter2,
                                                                 app(fun,x)),
                                                      fun)> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(cons,
                                                               x),
                                                              app(app(
                                                                   filter,
                                                                   fun),
                                                               xs))>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(filter2,
                                                                 app(fun,x)),
                                                      fun)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(filter2,
                                                                 app(fun,x)),
                                                      fun)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(filter2,
                                                              app(fun,x)),
                                                             fun)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(filter2,
                                                                 app(fun,x)),
                                                      fun)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  filter2,
                                                                  app(fun,x)),
                                                              fun),x)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(filter2,
                                                                 app(fun,x)),
                                                      fun)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  app(
                                                                   filter2,
                                                                   app(fun,x)),
                                                                  fun),
                                                              x),xs)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(filter2,
                                                                 app(fun,x)),
                                                      fun)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    map,
                                                                    fun),
                                                          xs)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(filter2,
                                                                 app(fun,x)),
                                                      fun)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(filter2,
                                                                 app(fun,x)),
                                                      fun)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    cons,
                                                                    app(fun,x)),
                                                          app(app(map,fun),xs))>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(filter2,
                                                                 app(fun,x)),
                                                      fun)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(f,
                                                                 x),u)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(filter2,
                                                                 app(fun,x)),
                                                      fun)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(f,x),
                                                                 u),z)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(filter2,
                                                                 app(fun,x)),
                                                      fun)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                 z),u)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(filter2,
                                                                 app(fun,x)),
                                                      fun)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(minus,
                                                                 y),x)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(filter2,
                                                                 app(fun,x)),
                                                      fun)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(f,
                                                                 app(s,x)),
                                                                app(app(
                                                                    minus,
                                                                    y),
                                                                 x))>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(filter2,
                                                                 app(fun,x)),
                                                      fun)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    f,
                                                                    app(s,x)),
                                                                 app(
                                                                  app(
                                                                   minus,
                                                                   y),
                                                                  x)),
                                                                z)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(filter2,
                                                                 app(fun,x)),
                                                      fun)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                 z),u)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(filter2,
                                                                 app(fun,x)),
                                                      fun)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(le,
                                                                 x),y)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(filter2,
                                                                 app(fun,x)),
                                                      fun)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(if,
                                                                 app(
                                                                  app(le,x),
                                                                  y)),
                                                                app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                                 u))>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(filter2,
                                                                 app(fun,x)),
                                                      fun)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                                 app(
                                                                  app(
                                                                   app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                   z),
                                                                  u)),
                                                                app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    z),
                                                                 u))>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(filter2,
                                                                 app(fun,x)),
                                                      fun)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(minus,z),
                                                         app(s,x))>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(filter2,
                                                                 app(fun,x)),
                                                      fun)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(f,x),u)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(filter2,
                                                                 app(fun,x)),
                                                      fun)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(
                                                                    app(f,x),
                                                                    u),
                                                         app(app(minus,z),
                                                          app(s,x)))>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(filter2,
                                                                 app(fun,x)),
                                                      fun)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    z),
                                                                    app(s,x))),
                                                         u)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(filter2,
                                                                 app(fun,x)),
                                                      fun)> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(f,x),app(s,0))>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(filter2,
                                                                 app(fun,x)),
                                                      fun)> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(f,x),app(s,0)),
                                           app(s,x))>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(filter2,
                                                                 app(fun,x)),
                                                      fun)> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(app(f,x),app(s,0)),
                                                      app(s,x)),app(s,x))>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(filter2,
                                                                 app(fun,x)),
                                                      fun)> 
     --> <Marked_app(app(le,app(s,x)),app(s,y)) , Marked_app(app(le,x),y)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(filter2,
                                                                 app(fun,x)),
                                                      fun)> 
     --> <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                 fun),
                                                      x)> 
     --> <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(
                                                               app(filter,
                                                                fun),
                                                               xs)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                 fun),
                                                      x)> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(filter,
                                                               fun),xs)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                 fun),
                                                      x)> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(cons,
                                                               x),
                                                              app(app(
                                                                   filter,
                                                                   fun),
                                                               xs))>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                 fun),
                                                      x)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                 fun),
                                                      x)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(filter2,
                                                              app(fun,x)),
                                                             fun)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                 fun),
                                                      x)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  filter2,
                                                                  app(fun,x)),
                                                              fun),x)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                 fun),
                                                      x)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  app(
                                                                   filter2,
                                                                   app(fun,x)),
                                                                  fun),
                                                              x),xs)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                 fun),
                                                      x)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    map,
                                                                    fun),
                                                          xs)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                 fun),
                                                      x)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                 fun),
                                                      x)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    cons,
                                                                    app(fun,x)),
                                                          app(app(map,fun),xs))>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                 fun),
                                                      x)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(f,
                                                                 x),u)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                 fun),
                                                      x)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(f,x),
                                                                 u),z)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                 fun),
                                                      x)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                 z),u)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                 fun),
                                                      x)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(minus,
                                                                 y),x)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                 fun),
                                                      x)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(f,
                                                                 app(s,x)),
                                                                app(app(
                                                                    minus,
                                                                    y),
                                                                 x))>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                 fun),
                                                      x)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    f,
                                                                    app(s,x)),
                                                                 app(
                                                                  app(
                                                                   minus,
                                                                   y),
                                                                  x)),
                                                                z)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                 fun),
                                                      x)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                 z),u)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                 fun),
                                                      x)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(le,
                                                                 x),y)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                 fun),
                                                      x)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(if,
                                                                 app(
                                                                  app(le,x),
                                                                  y)),
                                                                app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                                 u))>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                 fun),
                                                      x)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                                 app(
                                                                  app(
                                                                   app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                   z),
                                                                  u)),
                                                                app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    z),
                                                                 u))>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                 fun),
                                                      x)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(minus,z),
                                                         app(s,x))>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                 fun),
                                                      x)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(f,x),u)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                 fun),
                                                      x)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(
                                                                    app(f,x),
                                                                    u),
                                                         app(app(minus,z),
                                                          app(s,x)))>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                 fun),
                                                      x)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    z),
                                                                    app(s,x))),
                                                         u)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                 fun),
                                                      x)> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(f,x),app(s,0))>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                 fun),
                                                      x)> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(f,x),app(s,0)),
                                           app(s,x))>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                 fun),
                                                      x)> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(app(f,x),app(s,0)),
                                                      app(s,x)),app(s,x))>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                 fun),
                                                      x)> 
     --> <Marked_app(app(le,app(s,x)),app(s,y)) , Marked_app(app(le,x),y)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                 fun),
                                                      x)> 
     --> <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                    fun),
                                                                 x),xs)> 
     --> <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(
                                                               app(filter,
                                                                fun),
                                                               xs)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                    fun),
                                                                 x),xs)> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(filter,
                                                               fun),xs)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                    fun),
                                                                 x),xs)> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(cons,
                                                               x),
                                                              app(app(
                                                                   filter,
                                                                   fun),
                                                               xs))>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                    fun),
                                                                 x),xs)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                    fun),
                                                                 x),xs)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(filter2,
                                                              app(fun,x)),
                                                             fun)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                    fun),
                                                                 x),xs)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  filter2,
                                                                  app(fun,x)),
                                                              fun),x)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                    fun),
                                                                 x),xs)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  app(
                                                                   filter2,
                                                                   app(fun,x)),
                                                                  fun),
                                                              x),xs)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                    fun),
                                                                 x),xs)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    map,
                                                                    fun),
                                                          xs)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                    fun),
                                                                 x),xs)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                    fun),
                                                                 x),xs)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    cons,
                                                                    app(fun,x)),
                                                          app(app(map,fun),xs))>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                    fun),
                                                                 x),xs)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(f,
                                                                 x),u)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                    fun),
                                                                 x),xs)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(f,x),
                                                                 u),z)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                    fun),
                                                                 x),xs)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                 z),u)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                    fun),
                                                                 x),xs)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(minus,
                                                                 y),x)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                    fun),
                                                                 x),xs)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(f,
                                                                 app(s,x)),
                                                                app(app(
                                                                    minus,
                                                                    y),
                                                                 x))>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                    fun),
                                                                 x),xs)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    f,
                                                                    app(s,x)),
                                                                 app(
                                                                  app(
                                                                   minus,
                                                                   y),
                                                                  x)),
                                                                z)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                    fun),
                                                                 x),xs)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                 z),u)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                    fun),
                                                                 x),xs)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(le,
                                                                 x),y)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                    fun),
                                                                 x),xs)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(if,
                                                                 app(
                                                                  app(le,x),
                                                                  y)),
                                                                app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                                 u))>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                    fun),
                                                                 x),xs)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                                 app(
                                                                  app(
                                                                   app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                   z),
                                                                  u)),
                                                                app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    z),
                                                                 u))>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                    fun),
                                                                 x),xs)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(minus,z),
                                                         app(s,x))>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                    fun),
                                                                 x),xs)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(f,x),u)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                    fun),
                                                                 x),xs)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(
                                                                    app(f,x),
                                                                    u),
                                                         app(app(minus,z),
                                                          app(s,x)))>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                    fun),
                                                                 x),xs)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    z),
                                                                    app(s,x))),
                                                         u)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                    fun),
                                                                 x),xs)> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(f,x),app(s,0))>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                    fun),
                                                                 x),xs)> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(f,x),app(s,0)),
                                           app(s,x))>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                    fun),
                                                                 x),xs)> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(app(f,x),app(s,0)),
                                                      app(s,x)),app(s,x))>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                    fun),
                                                                 x),xs)> 
     --> <Marked_app(app(le,app(s,x)),app(s,y)) , Marked_app(app(le,x),y)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                    fun),
                                                                 x),xs)> 
     --> <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(map,fun),xs)> 
     --> <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(
                                                               app(filter,
                                                                fun),
                                                               xs)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(map,fun),xs)> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(filter,
                                                               fun),xs)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(map,fun),xs)> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(cons,
                                                               x),
                                                              app(app(
                                                                   filter,
                                                                   fun),
                                                               xs))>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(map,fun),xs)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(map,fun),xs)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(filter2,
                                                              app(fun,x)),
                                                             fun)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(map,fun),xs)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  filter2,
                                                                  app(fun,x)),
                                                              fun),x)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(map,fun),xs)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  app(
                                                                   filter2,
                                                                   app(fun,x)),
                                                                  fun),
                                                              x),xs)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(map,fun),xs)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    map,
                                                                    fun),
                                                          xs)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(map,fun),xs)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(map,fun),xs)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    cons,
                                                                    app(fun,x)),
                                                          app(app(map,fun),xs))>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(map,fun),xs)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(f,
                                                                 x),u)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(map,fun),xs)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(f,x),
                                                                 u),z)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(map,fun),xs)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                 z),u)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(map,fun),xs)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(minus,
                                                                 y),x)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(map,fun),xs)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(f,
                                                                 app(s,x)),
                                                                app(app(
                                                                    minus,
                                                                    y),
                                                                 x))>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(map,fun),xs)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    f,
                                                                    app(s,x)),
                                                                 app(
                                                                  app(
                                                                   minus,
                                                                   y),
                                                                  x)),
                                                                z)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(map,fun),xs)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                 z),u)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(map,fun),xs)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(le,
                                                                 x),y)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(map,fun),xs)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(if,
                                                                 app(
                                                                  app(le,x),
                                                                  y)),
                                                                app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                                 u))>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(map,fun),xs)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                                 app(
                                                                  app(
                                                                   app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                   z),
                                                                  u)),
                                                                app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    z),
                                                                 u))>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(map,fun),xs)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(minus,z),
                                                         app(s,x))>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(map,fun),xs)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(f,x),u)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(map,fun),xs)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(
                                                                    app(f,x),
                                                                    u),
                                                         app(app(minus,z),
                                                          app(s,x)))>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(map,fun),xs)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    z),
                                                                    app(s,x))),
                                                         u)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(map,fun),xs)> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(f,x),app(s,0))>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(map,fun),xs)> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(f,x),app(s,0)),
                                           app(s,x))>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(map,fun),xs)> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(app(f,x),app(s,0)),
                                                      app(s,x)),app(s,x))>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(map,fun),xs)> 
     --> <Marked_app(app(le,app(s,x)),app(s,y)) , Marked_app(app(le,x),y)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(map,fun),xs)> 
     --> <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(
                                                               app(filter,
                                                                fun),
                                                               xs)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(filter,
                                                               fun),xs)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(cons,
                                                               x),
                                                              app(app(
                                                                   filter,
                                                                   fun),
                                                               xs))>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(filter2,
                                                              app(fun,x)),
                                                             fun)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  filter2,
                                                                  app(fun,x)),
                                                              fun),x)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  app(
                                                                   filter2,
                                                                   app(fun,x)),
                                                                  fun),
                                                              x),xs)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    map,
                                                                    fun),
                                                          xs)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    cons,
                                                                    app(fun,x)),
                                                          app(app(map,fun),xs))>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(f,
                                                                 x),u)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(f,x),
                                                                 u),z)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                 z),u)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(minus,
                                                                 y),x)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(f,
                                                                 app(s,x)),
                                                                app(app(
                                                                    minus,
                                                                    y),
                                                                 x))>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    f,
                                                                    app(s,x)),
                                                                 app(
                                                                  app(
                                                                   minus,
                                                                   y),
                                                                  x)),
                                                                z)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                 z),u)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(le,
                                                                 x),y)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(if,
                                                                 app(
                                                                  app(le,x),
                                                                  y)),
                                                                app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                                 u))>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                                 app(
                                                                  app(
                                                                   app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                   z),
                                                                  u)),
                                                                app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    z),
                                                                 u))>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(minus,z),
                                                         app(s,x))>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(f,x),u)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(
                                                                    app(f,x),
                                                                    u),
                                                         app(app(minus,z),
                                                          app(s,x)))>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    z),
                                                                    app(s,x))),
                                                         u)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(f,x),app(s,0))>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(f,x),app(s,0)),
                                           app(s,x))>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(app(f,x),app(s,0)),
                                                      app(s,x)),app(s,x))>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(le,app(s,x)),app(s,y)) , Marked_app(app(le,x),y)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(cons,
                                                              app(fun,x)),
                                                   app(app(map,fun),xs))> 
     --> <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(
                                                               app(filter,
                                                                fun),
                                                               xs)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(cons,
                                                              app(fun,x)),
                                                   app(app(map,fun),xs))> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(filter,
                                                               fun),xs)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(cons,
                                                              app(fun,x)),
                                                   app(app(map,fun),xs))> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(cons,
                                                               x),
                                                              app(app(
                                                                   filter,
                                                                   fun),
                                                               xs))>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(cons,
                                                              app(fun,x)),
                                                   app(app(map,fun),xs))> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(cons,
                                                              app(fun,x)),
                                                   app(app(map,fun),xs))> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(filter2,
                                                              app(fun,x)),
                                                             fun)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(cons,
                                                              app(fun,x)),
                                                   app(app(map,fun),xs))> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  filter2,
                                                                  app(fun,x)),
                                                              fun),x)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(cons,
                                                              app(fun,x)),
                                                   app(app(map,fun),xs))> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  app(
                                                                   filter2,
                                                                   app(fun,x)),
                                                                  fun),
                                                              x),xs)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(cons,
                                                              app(fun,x)),
                                                   app(app(map,fun),xs))> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    map,
                                                                    fun),
                                                          xs)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(cons,
                                                              app(fun,x)),
                                                   app(app(map,fun),xs))> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(cons,
                                                              app(fun,x)),
                                                   app(app(map,fun),xs))> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    cons,
                                                                    app(fun,x)),
                                                          app(app(map,fun),xs))>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(cons,
                                                              app(fun,x)),
                                                   app(app(map,fun),xs))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(f,
                                                                 x),u)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(cons,
                                                              app(fun,x)),
                                                   app(app(map,fun),xs))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(f,x),
                                                                 u),z)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(cons,
                                                              app(fun,x)),
                                                   app(app(map,fun),xs))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                 z),u)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(cons,
                                                              app(fun,x)),
                                                   app(app(map,fun),xs))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(minus,
                                                                 y),x)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(cons,
                                                              app(fun,x)),
                                                   app(app(map,fun),xs))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(f,
                                                                 app(s,x)),
                                                                app(app(
                                                                    minus,
                                                                    y),
                                                                 x))>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(cons,
                                                              app(fun,x)),
                                                   app(app(map,fun),xs))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    f,
                                                                    app(s,x)),
                                                                 app(
                                                                  app(
                                                                   minus,
                                                                   y),
                                                                  x)),
                                                                z)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(cons,
                                                              app(fun,x)),
                                                   app(app(map,fun),xs))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                 z),u)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(cons,
                                                              app(fun,x)),
                                                   app(app(map,fun),xs))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(le,
                                                                 x),y)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(cons,
                                                              app(fun,x)),
                                                   app(app(map,fun),xs))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(if,
                                                                 app(
                                                                  app(le,x),
                                                                  y)),
                                                                app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                                 u))>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(cons,
                                                              app(fun,x)),
                                                   app(app(map,fun),xs))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                                 app(
                                                                  app(
                                                                   app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                   z),
                                                                  u)),
                                                                app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    z),
                                                                 u))>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(cons,
                                                              app(fun,x)),
                                                   app(app(map,fun),xs))> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(minus,z),
                                                         app(s,x))>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(cons,
                                                              app(fun,x)),
                                                   app(app(map,fun),xs))> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(f,x),u)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(cons,
                                                              app(fun,x)),
                                                   app(app(map,fun),xs))> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(
                                                                    app(f,x),
                                                                    u),
                                                         app(app(minus,z),
                                                          app(s,x)))>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(cons,
                                                              app(fun,x)),
                                                   app(app(map,fun),xs))> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    z),
                                                                    app(s,x))),
                                                         u)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(cons,
                                                              app(fun,x)),
                                                   app(app(map,fun),xs))> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(f,x),app(s,0))>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(cons,
                                                              app(fun,x)),
                                                   app(app(map,fun),xs))> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(f,x),app(s,0)),
                                           app(s,x))>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(cons,
                                                              app(fun,x)),
                                                   app(app(map,fun),xs))> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(app(f,x),app(s,0)),
                                                      app(s,x)),app(s,x))>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(cons,
                                                              app(fun,x)),
                                                   app(app(map,fun),xs))> 
     --> <Marked_app(app(le,app(s,x)),app(s,y)) , Marked_app(app(le,x),y)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(cons,
                                                              app(fun,x)),
                                                   app(app(map,fun),xs))> 
     --> <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(f,x),u)> 
     --> <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(
                                                               app(filter,
                                                                fun),
                                                               xs)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(f,x),u)> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(filter,
                                                               fun),xs)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(f,x),u)> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(cons,
                                                               x),
                                                              app(app(
                                                                   filter,
                                                                   fun),
                                                               xs))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(f,x),u)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(f,x),u)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(filter2,
                                                              app(fun,x)),
                                                             fun)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(f,x),u)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  filter2,
                                                                  app(fun,x)),
                                                              fun),x)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(f,x),u)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  app(
                                                                   filter2,
                                                                   app(fun,x)),
                                                                  fun),
                                                              x),xs)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(f,x),u)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    map,
                                                                    fun),
                                                          xs)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(f,x),u)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(f,x),u)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    cons,
                                                                    app(fun,x)),
                                                          app(app(map,fun),xs))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(f,x),u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(f,
                                                                 x),u)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(f,x),u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(f,x),
                                                                 u),z)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(f,x),u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                 z),u)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(f,x),u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(minus,
                                                                 y),x)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(f,x),u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(f,
                                                                 app(s,x)),
                                                                app(app(
                                                                    minus,
                                                                    y),
                                                                 x))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(f,x),u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    f,
                                                                    app(s,x)),
                                                                 app(
                                                                  app(
                                                                   minus,
                                                                   y),
                                                                  x)),
                                                                z)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(f,x),u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                 z),u)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(f,x),u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(le,
                                                                 x),y)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(f,x),u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(if,
                                                                 app(
                                                                  app(le,x),
                                                                  y)),
                                                                app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                                 u))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(f,x),u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                                 app(
                                                                  app(
                                                                   app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                   z),
                                                                  u)),
                                                                app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    z),
                                                                 u))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(f,x),u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(minus,z),
                                                         app(s,x))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(f,x),u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(f,x),u)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(f,x),u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(
                                                                    app(f,x),
                                                                    u),
                                                         app(app(minus,z),
                                                          app(s,x)))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(f,x),u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    z),
                                                                    app(s,x))),
                                                         u)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(f,x),u)> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(f,x),app(s,0))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(f,x),u)> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(f,x),app(s,0)),
                                           app(s,x))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(f,x),u)> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(app(f,x),app(s,0)),
                                                      app(s,x)),app(s,x))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(f,x),u)> 
     --> <Marked_app(app(le,app(s,x)),app(s,y)) , Marked_app(app(le,x),y)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(f,x),u)> 
     --> <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(f,x),
                                                                    u),
                                                         z)> 
     --> <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(
                                                               app(filter,
                                                                fun),
                                                               xs)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(f,x),
                                                                    u),
                                                         z)> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(filter,
                                                               fun),xs)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(f,x),
                                                                    u),
                                                         z)> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(cons,
                                                               x),
                                                              app(app(
                                                                   filter,
                                                                   fun),
                                                               xs))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(f,x),
                                                                    u),
                                                         z)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(f,x),
                                                                    u),
                                                         z)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(filter2,
                                                              app(fun,x)),
                                                             fun)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(f,x),
                                                                    u),
                                                         z)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  filter2,
                                                                  app(fun,x)),
                                                              fun),x)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(f,x),
                                                                    u),
                                                         z)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  app(
                                                                   filter2,
                                                                   app(fun,x)),
                                                                  fun),
                                                              x),xs)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(f,x),
                                                                    u),
                                                         z)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    map,
                                                                    fun),
                                                          xs)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(f,x),
                                                                    u),
                                                         z)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(f,x),
                                                                    u),
                                                         z)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    cons,
                                                                    app(fun,x)),
                                                          app(app(map,fun),xs))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(f,x),
                                                                    u),
                                                         z)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(f,
                                                                 x),u)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(f,x),
                                                                    u),
                                                         z)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(f,x),
                                                                 u),z)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(f,x),
                                                                    u),
                                                         z)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                 z),u)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(f,x),
                                                                    u),
                                                         z)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(minus,
                                                                 y),x)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(f,x),
                                                                    u),
                                                         z)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(f,
                                                                 app(s,x)),
                                                                app(app(
                                                                    minus,
                                                                    y),
                                                                 x))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(f,x),
                                                                    u),
                                                         z)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    f,
                                                                    app(s,x)),
                                                                 app(
                                                                  app(
                                                                   minus,
                                                                   y),
                                                                  x)),
                                                                z)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(f,x),
                                                                    u),
                                                         z)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                 z),u)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(f,x),
                                                                    u),
                                                         z)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(le,
                                                                 x),y)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(f,x),
                                                                    u),
                                                         z)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(if,
                                                                 app(
                                                                  app(le,x),
                                                                  y)),
                                                                app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                                 u))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(f,x),
                                                                    u),
                                                         z)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                                 app(
                                                                  app(
                                                                   app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                   z),
                                                                  u)),
                                                                app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    z),
                                                                 u))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(f,x),
                                                                    u),
                                                         z)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(minus,z),
                                                         app(s,x))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(f,x),
                                                                    u),
                                                         z)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(f,x),u)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(f,x),
                                                                    u),
                                                         z)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(
                                                                    app(f,x),
                                                                    u),
                                                         app(app(minus,z),
                                                          app(s,x)))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(f,x),
                                                                    u),
                                                         z)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    z),
                                                                    app(s,x))),
                                                         u)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(f,x),
                                                                    u),
                                                         z)> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(f,x),app(s,0))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(f,x),
                                                                    u),
                                                         z)> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(f,x),app(s,0)),
                                           app(s,x))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(f,x),
                                                                    u),
                                                         z)> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(app(f,x),app(s,0)),
                                                      app(s,x)),app(s,x))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(f,x),
                                                                    u),
                                                         z)> 
     --> <Marked_app(app(le,app(s,x)),app(s,y)) , Marked_app(app(le,x),y)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(f,x),
                                                                    u),
                                                         z)> 
     --> <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    z),
                                                         u)> 
     --> <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(
                                                               app(filter,
                                                                fun),
                                                               xs)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    z),
                                                         u)> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(filter,
                                                               fun),xs)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    z),
                                                         u)> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(cons,
                                                               x),
                                                              app(app(
                                                                   filter,
                                                                   fun),
                                                               xs))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    z),
                                                         u)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    z),
                                                         u)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(filter2,
                                                              app(fun,x)),
                                                             fun)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    z),
                                                         u)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  filter2,
                                                                  app(fun,x)),
                                                              fun),x)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    z),
                                                         u)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  app(
                                                                   filter2,
                                                                   app(fun,x)),
                                                                  fun),
                                                              x),xs)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    z),
                                                         u)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    map,
                                                                    fun),
                                                          xs)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    z),
                                                         u)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    z),
                                                         u)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    cons,
                                                                    app(fun,x)),
                                                          app(app(map,fun),xs))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    z),
                                                         u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(f,
                                                                 x),u)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    z),
                                                         u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(f,x),
                                                                 u),z)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    z),
                                                         u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                 z),u)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    z),
                                                         u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(minus,
                                                                 y),x)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    z),
                                                         u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(f,
                                                                 app(s,x)),
                                                                app(app(
                                                                    minus,
                                                                    y),
                                                                 x))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    z),
                                                         u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    f,
                                                                    app(s,x)),
                                                                 app(
                                                                  app(
                                                                   minus,
                                                                   y),
                                                                  x)),
                                                                z)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    z),
                                                         u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                 z),u)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    z),
                                                         u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(le,
                                                                 x),y)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    z),
                                                         u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(if,
                                                                 app(
                                                                  app(le,x),
                                                                  y)),
                                                                app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                                 u))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    z),
                                                         u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                                 app(
                                                                  app(
                                                                   app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                   z),
                                                                  u)),
                                                                app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    z),
                                                                 u))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    z),
                                                         u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(minus,z),
                                                         app(s,x))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    z),
                                                         u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(f,x),u)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    z),
                                                         u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(
                                                                    app(f,x),
                                                                    u),
                                                         app(app(minus,z),
                                                          app(s,x)))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    z),
                                                         u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    z),
                                                                    app(s,x))),
                                                         u)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    z),
                                                         u)> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(f,x),app(s,0))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    z),
                                                         u)> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(f,x),app(s,0)),
                                           app(s,x))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    z),
                                                         u)> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(app(f,x),app(s,0)),
                                                      app(s,x)),app(s,x))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    z),
                                                         u)> 
     --> <Marked_app(app(le,app(s,x)),app(s,y)) , Marked_app(app(le,x),y)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    z),
                                                         u)> 
     --> <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(minus,y),
                                                         x)> 
     --> <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(
                                                               app(filter,
                                                                fun),
                                                               xs)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(minus,y),
                                                         x)> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(filter,
                                                               fun),xs)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(minus,y),
                                                         x)> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(cons,
                                                               x),
                                                              app(app(
                                                                   filter,
                                                                   fun),
                                                               xs))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(minus,y),
                                                         x)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(minus,y),
                                                         x)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(filter2,
                                                              app(fun,x)),
                                                             fun)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(minus,y),
                                                         x)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  filter2,
                                                                  app(fun,x)),
                                                              fun),x)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(minus,y),
                                                         x)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  app(
                                                                   filter2,
                                                                   app(fun,x)),
                                                                  fun),
                                                              x),xs)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(minus,y),
                                                         x)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    map,
                                                                    fun),
                                                          xs)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(minus,y),
                                                         x)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(minus,y),
                                                         x)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    cons,
                                                                    app(fun,x)),
                                                          app(app(map,fun),xs))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(minus,y),
                                                         x)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(f,
                                                                 x),u)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(minus,y),
                                                         x)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(f,x),
                                                                 u),z)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(minus,y),
                                                         x)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                 z),u)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(minus,y),
                                                         x)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(minus,
                                                                 y),x)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(minus,y),
                                                         x)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(f,
                                                                 app(s,x)),
                                                                app(app(
                                                                    minus,
                                                                    y),
                                                                 x))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(minus,y),
                                                         x)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    f,
                                                                    app(s,x)),
                                                                 app(
                                                                  app(
                                                                   minus,
                                                                   y),
                                                                  x)),
                                                                z)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(minus,y),
                                                         x)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                 z),u)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(minus,y),
                                                         x)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(le,
                                                                 x),y)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(minus,y),
                                                         x)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(if,
                                                                 app(
                                                                  app(le,x),
                                                                  y)),
                                                                app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                                 u))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(minus,y),
                                                         x)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                                 app(
                                                                  app(
                                                                   app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                   z),
                                                                  u)),
                                                                app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    z),
                                                                 u))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(minus,y),
                                                         x)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(minus,z),
                                                         app(s,x))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(minus,y),
                                                         x)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(f,x),u)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(minus,y),
                                                         x)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(
                                                                    app(f,x),
                                                                    u),
                                                         app(app(minus,z),
                                                          app(s,x)))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(minus,y),
                                                         x)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    z),
                                                                    app(s,x))),
                                                         u)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(minus,y),
                                                         x)> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(f,x),app(s,0))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(minus,y),
                                                         x)> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(f,x),app(s,0)),
                                           app(s,x))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(minus,y),
                                                         x)> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(app(f,x),app(s,0)),
                                                      app(s,x)),app(s,x))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(minus,y),
                                                         x)> 
     --> <Marked_app(app(le,app(s,x)),app(s,y)) , Marked_app(app(le,x),y)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(minus,y),
                                                         x)> 
     --> <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    f,
                                                                    app(s,x)),
                                                         app(app(minus,y),x))> 
     --> <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(
                                                               app(filter,
                                                                fun),
                                                               xs)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    f,
                                                                    app(s,x)),
                                                         app(app(minus,y),x))> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(filter,
                                                               fun),xs)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    f,
                                                                    app(s,x)),
                                                         app(app(minus,y),x))> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(cons,
                                                               x),
                                                              app(app(
                                                                   filter,
                                                                   fun),
                                                               xs))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    f,
                                                                    app(s,x)),
                                                         app(app(minus,y),x))> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    f,
                                                                    app(s,x)),
                                                         app(app(minus,y),x))> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(filter2,
                                                              app(fun,x)),
                                                             fun)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    f,
                                                                    app(s,x)),
                                                         app(app(minus,y),x))> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  filter2,
                                                                  app(fun,x)),
                                                              fun),x)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    f,
                                                                    app(s,x)),
                                                         app(app(minus,y),x))> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  app(
                                                                   filter2,
                                                                   app(fun,x)),
                                                                  fun),
                                                              x),xs)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    f,
                                                                    app(s,x)),
                                                         app(app(minus,y),x))> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    map,
                                                                    fun),
                                                          xs)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    f,
                                                                    app(s,x)),
                                                         app(app(minus,y),x))> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    f,
                                                                    app(s,x)),
                                                         app(app(minus,y),x))> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    cons,
                                                                    app(fun,x)),
                                                          app(app(map,fun),xs))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    f,
                                                                    app(s,x)),
                                                         app(app(minus,y),x))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(f,
                                                                 x),u)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    f,
                                                                    app(s,x)),
                                                         app(app(minus,y),x))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(f,x),
                                                                 u),z)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    f,
                                                                    app(s,x)),
                                                         app(app(minus,y),x))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                 z),u)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    f,
                                                                    app(s,x)),
                                                         app(app(minus,y),x))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(minus,
                                                                 y),x)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    f,
                                                                    app(s,x)),
                                                         app(app(minus,y),x))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(f,
                                                                 app(s,x)),
                                                                app(app(
                                                                    minus,
                                                                    y),
                                                                 x))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    f,
                                                                    app(s,x)),
                                                         app(app(minus,y),x))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    f,
                                                                    app(s,x)),
                                                                 app(
                                                                  app(
                                                                   minus,
                                                                   y),
                                                                  x)),
                                                                z)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    f,
                                                                    app(s,x)),
                                                         app(app(minus,y),x))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                 z),u)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    f,
                                                                    app(s,x)),
                                                         app(app(minus,y),x))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(le,
                                                                 x),y)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    f,
                                                                    app(s,x)),
                                                         app(app(minus,y),x))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(if,
                                                                 app(
                                                                  app(le,x),
                                                                  y)),
                                                                app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                                 u))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    f,
                                                                    app(s,x)),
                                                         app(app(minus,y),x))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                                 app(
                                                                  app(
                                                                   app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                   z),
                                                                  u)),
                                                                app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    z),
                                                                 u))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    f,
                                                                    app(s,x)),
                                                         app(app(minus,y),x))> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(minus,z),
                                                         app(s,x))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    f,
                                                                    app(s,x)),
                                                         app(app(minus,y),x))> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(f,x),u)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    f,
                                                                    app(s,x)),
                                                         app(app(minus,y),x))> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(
                                                                    app(f,x),
                                                                    u),
                                                         app(app(minus,z),
                                                          app(s,x)))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    f,
                                                                    app(s,x)),
                                                         app(app(minus,y),x))> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    z),
                                                                    app(s,x))),
                                                         u)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    f,
                                                                    app(s,x)),
                                                         app(app(minus,y),x))> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(f,x),app(s,0))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    f,
                                                                    app(s,x)),
                                                         app(app(minus,y),x))> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(f,x),app(s,0)),
                                           app(s,x))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    f,
                                                                    app(s,x)),
                                                         app(app(minus,y),x))> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(app(f,x),app(s,0)),
                                                      app(s,x)),app(s,x))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    f,
                                                                    app(s,x)),
                                                         app(app(minus,y),x))> 
     --> <Marked_app(app(le,app(s,x)),app(s,y)) , Marked_app(app(le,x),y)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    f,
                                                                    app(s,x)),
                                                         app(app(minus,y),x))> 
     --> <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                         z)> 
     --> <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(
                                                               app(filter,
                                                                fun),
                                                               xs)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                         z)> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(filter,
                                                               fun),xs)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                         z)> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(cons,
                                                               x),
                                                              app(app(
                                                                   filter,
                                                                   fun),
                                                               xs))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                         z)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                         z)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(filter2,
                                                              app(fun,x)),
                                                             fun)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                         z)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  filter2,
                                                                  app(fun,x)),
                                                              fun),x)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                         z)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  app(
                                                                   filter2,
                                                                   app(fun,x)),
                                                                  fun),
                                                              x),xs)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                         z)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    map,
                                                                    fun),
                                                          xs)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                         z)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                         z)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    cons,
                                                                    app(fun,x)),
                                                          app(app(map,fun),xs))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                         z)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(f,
                                                                 x),u)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                         z)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(f,x),
                                                                 u),z)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                         z)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                 z),u)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                         z)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(minus,
                                                                 y),x)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                         z)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(f,
                                                                 app(s,x)),
                                                                app(app(
                                                                    minus,
                                                                    y),
                                                                 x))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                         z)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    f,
                                                                    app(s,x)),
                                                                 app(
                                                                  app(
                                                                   minus,
                                                                   y),
                                                                  x)),
                                                                z)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                         z)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                 z),u)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                         z)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(le,
                                                                 x),y)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                         z)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(if,
                                                                 app(
                                                                  app(le,x),
                                                                  y)),
                                                                app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                                 u))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                         z)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                                 app(
                                                                  app(
                                                                   app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                   z),
                                                                  u)),
                                                                app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    z),
                                                                 u))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                         z)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(minus,z),
                                                         app(s,x))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                         z)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(f,x),u)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                         z)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(
                                                                    app(f,x),
                                                                    u),
                                                         app(app(minus,z),
                                                          app(s,x)))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                         z)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    z),
                                                                    app(s,x))),
                                                         u)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                         z)> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(f,x),app(s,0))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                         z)> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(f,x),app(s,0)),
                                           app(s,x))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                         z)> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(app(f,x),app(s,0)),
                                                      app(s,x)),app(s,x))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                         z)> 
     --> <Marked_app(app(le,app(s,x)),app(s,y)) , Marked_app(app(le,x),y)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                         z)> 
     --> <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                         u)> 
     --> <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(
                                                               app(filter,
                                                                fun),
                                                               xs)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                         u)> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(filter,
                                                               fun),xs)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                         u)> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(cons,
                                                               x),
                                                              app(app(
                                                                   filter,
                                                                   fun),
                                                               xs))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                         u)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                         u)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(filter2,
                                                              app(fun,x)),
                                                             fun)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                         u)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  filter2,
                                                                  app(fun,x)),
                                                              fun),x)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                         u)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  app(
                                                                   filter2,
                                                                   app(fun,x)),
                                                                  fun),
                                                              x),xs)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                         u)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    map,
                                                                    fun),
                                                          xs)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                         u)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                         u)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    cons,
                                                                    app(fun,x)),
                                                          app(app(map,fun),xs))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                         u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(f,
                                                                 x),u)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                         u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(f,x),
                                                                 u),z)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                         u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                 z),u)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                         u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(minus,
                                                                 y),x)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                         u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(f,
                                                                 app(s,x)),
                                                                app(app(
                                                                    minus,
                                                                    y),
                                                                 x))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                         u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    f,
                                                                    app(s,x)),
                                                                 app(
                                                                  app(
                                                                   minus,
                                                                   y),
                                                                  x)),
                                                                z)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                         u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                 z),u)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                         u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(le,
                                                                 x),y)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                         u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(if,
                                                                 app(
                                                                  app(le,x),
                                                                  y)),
                                                                app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                                 u))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                         u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                                 app(
                                                                  app(
                                                                   app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                   z),
                                                                  u)),
                                                                app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    z),
                                                                 u))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                         u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(minus,z),
                                                         app(s,x))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                         u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(f,x),u)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                         u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(
                                                                    app(f,x),
                                                                    u),
                                                         app(app(minus,z),
                                                          app(s,x)))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                         u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    z),
                                                                    app(s,x))),
                                                         u)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                         u)> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(f,x),app(s,0))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                         u)> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(f,x),app(s,0)),
                                           app(s,x))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                         u)> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(app(f,x),app(s,0)),
                                                      app(s,x)),app(s,x))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                         u)> 
     --> <Marked_app(app(le,app(s,x)),app(s,y)) , Marked_app(app(le,x),y)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                         u)> 
     --> <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(le,x),y)> 
     --> <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(
                                                               app(filter,
                                                                fun),
                                                               xs)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(le,x),y)> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(filter,
                                                               fun),xs)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(le,x),y)> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(cons,
                                                               x),
                                                              app(app(
                                                                   filter,
                                                                   fun),
                                                               xs))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(le,x),y)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(le,x),y)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(filter2,
                                                              app(fun,x)),
                                                             fun)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(le,x),y)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  filter2,
                                                                  app(fun,x)),
                                                              fun),x)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(le,x),y)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  app(
                                                                   filter2,
                                                                   app(fun,x)),
                                                                  fun),
                                                              x),xs)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(le,x),y)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    map,
                                                                    fun),
                                                          xs)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(le,x),y)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(le,x),y)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    cons,
                                                                    app(fun,x)),
                                                          app(app(map,fun),xs))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(le,x),y)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(f,
                                                                 x),u)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(le,x),y)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(f,x),
                                                                 u),z)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(le,x),y)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                 z),u)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(le,x),y)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(minus,
                                                                 y),x)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(le,x),y)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(f,
                                                                 app(s,x)),
                                                                app(app(
                                                                    minus,
                                                                    y),
                                                                 x))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(le,x),y)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    f,
                                                                    app(s,x)),
                                                                 app(
                                                                  app(
                                                                   minus,
                                                                   y),
                                                                  x)),
                                                                z)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(le,x),y)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                 z),u)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(le,x),y)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(le,
                                                                 x),y)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(le,x),y)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(if,
                                                                 app(
                                                                  app(le,x),
                                                                  y)),
                                                                app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                                 u))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(le,x),y)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                                 app(
                                                                  app(
                                                                   app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                   z),
                                                                  u)),
                                                                app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    z),
                                                                 u))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(le,x),y)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(minus,z),
                                                         app(s,x))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(le,x),y)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(f,x),u)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(le,x),y)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(
                                                                    app(f,x),
                                                                    u),
                                                         app(app(minus,z),
                                                          app(s,x)))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(le,x),y)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    z),
                                                                    app(s,x))),
                                                         u)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(le,x),y)> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(f,x),app(s,0))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(le,x),y)> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(f,x),app(s,0)),
                                           app(s,x))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(le,x),y)> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(app(f,x),app(s,0)),
                                                      app(s,x)),app(s,x))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(le,x),y)> 
     --> <Marked_app(app(le,app(s,x)),app(s,y)) , Marked_app(app(le,x),y)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(le,x),y)> 
     --> <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                         app(app(app(
                                                                  app(
                                                                   f,
                                                                   app(s,x)),
                                                                  app(
                                                                   app(
                                                                    minus,
                                                                    y),
                                                                   x)),
                                                              z),u))> 
     --> <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(
                                                               app(filter,
                                                                fun),
                                                               xs)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                         app(app(app(
                                                                  app(
                                                                   f,
                                                                   app(s,x)),
                                                                  app(
                                                                   app(
                                                                    minus,
                                                                    y),
                                                                   x)),
                                                              z),u))> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(filter,
                                                               fun),xs)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                         app(app(app(
                                                                  app(
                                                                   f,
                                                                   app(s,x)),
                                                                  app(
                                                                   app(
                                                                    minus,
                                                                    y),
                                                                   x)),
                                                              z),u))> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(cons,
                                                               x),
                                                              app(app(
                                                                   filter,
                                                                   fun),
                                                               xs))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                         app(app(app(
                                                                  app(
                                                                   f,
                                                                   app(s,x)),
                                                                  app(
                                                                   app(
                                                                    minus,
                                                                    y),
                                                                   x)),
                                                              z),u))> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                         app(app(app(
                                                                  app(
                                                                   f,
                                                                   app(s,x)),
                                                                  app(
                                                                   app(
                                                                    minus,
                                                                    y),
                                                                   x)),
                                                              z),u))> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(filter2,
                                                              app(fun,x)),
                                                             fun)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                         app(app(app(
                                                                  app(
                                                                   f,
                                                                   app(s,x)),
                                                                  app(
                                                                   app(
                                                                    minus,
                                                                    y),
                                                                   x)),
                                                              z),u))> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  filter2,
                                                                  app(fun,x)),
                                                              fun),x)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                         app(app(app(
                                                                  app(
                                                                   f,
                                                                   app(s,x)),
                                                                  app(
                                                                   app(
                                                                    minus,
                                                                    y),
                                                                   x)),
                                                              z),u))> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  app(
                                                                   filter2,
                                                                   app(fun,x)),
                                                                  fun),
                                                              x),xs)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                         app(app(app(
                                                                  app(
                                                                   f,
                                                                   app(s,x)),
                                                                  app(
                                                                   app(
                                                                    minus,
                                                                    y),
                                                                   x)),
                                                              z),u))> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    map,
                                                                    fun),
                                                          xs)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                         app(app(app(
                                                                  app(
                                                                   f,
                                                                   app(s,x)),
                                                                  app(
                                                                   app(
                                                                    minus,
                                                                    y),
                                                                   x)),
                                                              z),u))> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                         app(app(app(
                                                                  app(
                                                                   f,
                                                                   app(s,x)),
                                                                  app(
                                                                   app(
                                                                    minus,
                                                                    y),
                                                                   x)),
                                                              z),u))> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    cons,
                                                                    app(fun,x)),
                                                          app(app(map,fun),xs))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                         app(app(app(
                                                                  app(
                                                                   f,
                                                                   app(s,x)),
                                                                  app(
                                                                   app(
                                                                    minus,
                                                                    y),
                                                                   x)),
                                                              z),u))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(f,
                                                                 x),u)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                         app(app(app(
                                                                  app(
                                                                   f,
                                                                   app(s,x)),
                                                                  app(
                                                                   app(
                                                                    minus,
                                                                    y),
                                                                   x)),
                                                              z),u))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(f,x),
                                                                 u),z)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                         app(app(app(
                                                                  app(
                                                                   f,
                                                                   app(s,x)),
                                                                  app(
                                                                   app(
                                                                    minus,
                                                                    y),
                                                                   x)),
                                                              z),u))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                 z),u)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                         app(app(app(
                                                                  app(
                                                                   f,
                                                                   app(s,x)),
                                                                  app(
                                                                   app(
                                                                    minus,
                                                                    y),
                                                                   x)),
                                                              z),u))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(minus,
                                                                 y),x)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                         app(app(app(
                                                                  app(
                                                                   f,
                                                                   app(s,x)),
                                                                  app(
                                                                   app(
                                                                    minus,
                                                                    y),
                                                                   x)),
                                                              z),u))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(f,
                                                                 app(s,x)),
                                                                app(app(
                                                                    minus,
                                                                    y),
                                                                 x))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                         app(app(app(
                                                                  app(
                                                                   f,
                                                                   app(s,x)),
                                                                  app(
                                                                   app(
                                                                    minus,
                                                                    y),
                                                                   x)),
                                                              z),u))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    f,
                                                                    app(s,x)),
                                                                 app(
                                                                  app(
                                                                   minus,
                                                                   y),
                                                                  x)),
                                                                z)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                         app(app(app(
                                                                  app(
                                                                   f,
                                                                   app(s,x)),
                                                                  app(
                                                                   app(
                                                                    minus,
                                                                    y),
                                                                   x)),
                                                              z),u))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                 z),u)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                         app(app(app(
                                                                  app(
                                                                   f,
                                                                   app(s,x)),
                                                                  app(
                                                                   app(
                                                                    minus,
                                                                    y),
                                                                   x)),
                                                              z),u))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(le,
                                                                 x),y)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                         app(app(app(
                                                                  app(
                                                                   f,
                                                                   app(s,x)),
                                                                  app(
                                                                   app(
                                                                    minus,
                                                                    y),
                                                                   x)),
                                                              z),u))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(if,
                                                                 app(
                                                                  app(le,x),
                                                                  y)),
                                                                app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                                 u))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                         app(app(app(
                                                                  app(
                                                                   f,
                                                                   app(s,x)),
                                                                  app(
                                                                   app(
                                                                    minus,
                                                                    y),
                                                                   x)),
                                                              z),u))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                                 app(
                                                                  app(
                                                                   app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                   z),
                                                                  u)),
                                                                app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    z),
                                                                 u))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                         app(app(app(
                                                                  app(
                                                                   f,
                                                                   app(s,x)),
                                                                  app(
                                                                   app(
                                                                    minus,
                                                                    y),
                                                                   x)),
                                                              z),u))> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(minus,z),
                                                         app(s,x))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                         app(app(app(
                                                                  app(
                                                                   f,
                                                                   app(s,x)),
                                                                  app(
                                                                   app(
                                                                    minus,
                                                                    y),
                                                                   x)),
                                                              z),u))> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(f,x),u)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                         app(app(app(
                                                                  app(
                                                                   f,
                                                                   app(s,x)),
                                                                  app(
                                                                   app(
                                                                    minus,
                                                                    y),
                                                                   x)),
                                                              z),u))> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(
                                                                    app(f,x),
                                                                    u),
                                                         app(app(minus,z),
                                                          app(s,x)))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                         app(app(app(
                                                                  app(
                                                                   f,
                                                                   app(s,x)),
                                                                  app(
                                                                   app(
                                                                    minus,
                                                                    y),
                                                                   x)),
                                                              z),u))> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    z),
                                                                    app(s,x))),
                                                         u)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                         app(app(app(
                                                                  app(
                                                                   f,
                                                                   app(s,x)),
                                                                  app(
                                                                   app(
                                                                    minus,
                                                                    y),
                                                                   x)),
                                                              z),u))> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(f,x),app(s,0))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                         app(app(app(
                                                                  app(
                                                                   f,
                                                                   app(s,x)),
                                                                  app(
                                                                   app(
                                                                    minus,
                                                                    y),
                                                                   x)),
                                                              z),u))> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(f,x),app(s,0)),
                                           app(s,x))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                         app(app(app(
                                                                  app(
                                                                   f,
                                                                   app(s,x)),
                                                                  app(
                                                                   app(
                                                                    minus,
                                                                    y),
                                                                   x)),
                                                              z),u))> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(app(f,x),app(s,0)),
                                                      app(s,x)),app(s,x))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                         app(app(app(
                                                                  app(
                                                                   f,
                                                                   app(s,x)),
                                                                  app(
                                                                   app(
                                                                    minus,
                                                                    y),
                                                                   x)),
                                                              z),u))> 
     --> <Marked_app(app(le,app(s,x)),app(s,y)) , Marked_app(app(le,x),y)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                         app(app(app(
                                                                  app(
                                                                   f,
                                                                   app(s,x)),
                                                                  app(
                                                                   app(
                                                                    minus,
                                                                    y),
                                                                   x)),
                                                              z),u))> 
     --> <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                                    u)),
                                                         app(app(app(
                                                                  app(f,x),
                                                                  u),
                                                              z),u))> 
     --> <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(
                                                               app(filter,
                                                                fun),
                                                               xs)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                                    u)),
                                                         app(app(app(
                                                                  app(f,x),
                                                                  u),
                                                              z),u))> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(filter,
                                                               fun),xs)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                                    u)),
                                                         app(app(app(
                                                                  app(f,x),
                                                                  u),
                                                              z),u))> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(cons,
                                                               x),
                                                              app(app(
                                                                   filter,
                                                                   fun),
                                                               xs))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                                    u)),
                                                         app(app(app(
                                                                  app(f,x),
                                                                  u),
                                                              z),u))> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                                    u)),
                                                         app(app(app(
                                                                  app(f,x),
                                                                  u),
                                                              z),u))> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(filter2,
                                                              app(fun,x)),
                                                             fun)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                                    u)),
                                                         app(app(app(
                                                                  app(f,x),
                                                                  u),
                                                              z),u))> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  filter2,
                                                                  app(fun,x)),
                                                              fun),x)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                                    u)),
                                                         app(app(app(
                                                                  app(f,x),
                                                                  u),
                                                              z),u))> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  app(
                                                                   filter2,
                                                                   app(fun,x)),
                                                                  fun),
                                                              x),xs)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                                    u)),
                                                         app(app(app(
                                                                  app(f,x),
                                                                  u),
                                                              z),u))> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    map,
                                                                    fun),
                                                          xs)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                                    u)),
                                                         app(app(app(
                                                                  app(f,x),
                                                                  u),
                                                              z),u))> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                                    u)),
                                                         app(app(app(
                                                                  app(f,x),
                                                                  u),
                                                              z),u))> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    cons,
                                                                    app(fun,x)),
                                                          app(app(map,fun),xs))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                                    u)),
                                                         app(app(app(
                                                                  app(f,x),
                                                                  u),
                                                              z),u))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(f,
                                                                 x),u)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                                    u)),
                                                         app(app(app(
                                                                  app(f,x),
                                                                  u),
                                                              z),u))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(f,x),
                                                                 u),z)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                                    u)),
                                                         app(app(app(
                                                                  app(f,x),
                                                                  u),
                                                              z),u))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                 z),u)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                                    u)),
                                                         app(app(app(
                                                                  app(f,x),
                                                                  u),
                                                              z),u))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(minus,
                                                                 y),x)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                                    u)),
                                                         app(app(app(
                                                                  app(f,x),
                                                                  u),
                                                              z),u))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(f,
                                                                 app(s,x)),
                                                                app(app(
                                                                    minus,
                                                                    y),
                                                                 x))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                                    u)),
                                                         app(app(app(
                                                                  app(f,x),
                                                                  u),
                                                              z),u))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    f,
                                                                    app(s,x)),
                                                                 app(
                                                                  app(
                                                                   minus,
                                                                   y),
                                                                  x)),
                                                                z)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                                    u)),
                                                         app(app(app(
                                                                  app(f,x),
                                                                  u),
                                                              z),u))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                 z),u)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                                    u)),
                                                         app(app(app(
                                                                  app(f,x),
                                                                  u),
                                                              z),u))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(le,
                                                                 x),y)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                                    u)),
                                                         app(app(app(
                                                                  app(f,x),
                                                                  u),
                                                              z),u))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(if,
                                                                 app(
                                                                  app(le,x),
                                                                  y)),
                                                                app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                                 u))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                                    u)),
                                                         app(app(app(
                                                                  app(f,x),
                                                                  u),
                                                              z),u))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                                 app(
                                                                  app(
                                                                   app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                   z),
                                                                  u)),
                                                                app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    z),
                                                                 u))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                                    u)),
                                                         app(app(app(
                                                                  app(f,x),
                                                                  u),
                                                              z),u))> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(minus,z),
                                                         app(s,x))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                                    u)),
                                                         app(app(app(
                                                                  app(f,x),
                                                                  u),
                                                              z),u))> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(f,x),u)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                                    u)),
                                                         app(app(app(
                                                                  app(f,x),
                                                                  u),
                                                              z),u))> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(
                                                                    app(f,x),
                                                                    u),
                                                         app(app(minus,z),
                                                          app(s,x)))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                                    u)),
                                                         app(app(app(
                                                                  app(f,x),
                                                                  u),
                                                              z),u))> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    z),
                                                                    app(s,x))),
                                                         u)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                                    u)),
                                                         app(app(app(
                                                                  app(f,x),
                                                                  u),
                                                              z),u))> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(f,x),app(s,0))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                                    u)),
                                                         app(app(app(
                                                                  app(f,x),
                                                                  u),
                                                              z),u))> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(f,x),app(s,0)),
                                           app(s,x))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                                    u)),
                                                         app(app(app(
                                                                  app(f,x),
                                                                  u),
                                                              z),u))> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(app(f,x),app(s,0)),
                                                      app(s,x)),app(s,x))>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                                    u)),
                                                         app(app(app(
                                                                  app(f,x),
                                                                  u),
                                                              z),u))> 
     --> <Marked_app(app(le,app(s,x)),app(s,y)) , Marked_app(app(le,x),y)>
  <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                                    u)),
                                                         app(app(app(
                                                                  app(f,x),
                                                                  u),
                                                              z),u))> 
     --> <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(minus,z),
                                                  app(s,x))> 
     --> <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(
                                                               app(filter,
                                                                fun),
                                                               xs)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(minus,z),
                                                  app(s,x))> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(filter,
                                                               fun),xs)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(minus,z),
                                                  app(s,x))> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(cons,
                                                               x),
                                                              app(app(
                                                                   filter,
                                                                   fun),
                                                               xs))>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(minus,z),
                                                  app(s,x))> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(minus,z),
                                                  app(s,x))> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(filter2,
                                                              app(fun,x)),
                                                             fun)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(minus,z),
                                                  app(s,x))> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  filter2,
                                                                  app(fun,x)),
                                                              fun),x)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(minus,z),
                                                  app(s,x))> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  app(
                                                                   filter2,
                                                                   app(fun,x)),
                                                                  fun),
                                                              x),xs)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(minus,z),
                                                  app(s,x))> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    map,
                                                                    fun),
                                                          xs)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(minus,z),
                                                  app(s,x))> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(minus,z),
                                                  app(s,x))> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    cons,
                                                                    app(fun,x)),
                                                          app(app(map,fun),xs))>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(minus,z),
                                                  app(s,x))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(f,
                                                                 x),u)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(minus,z),
                                                  app(s,x))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(f,x),
                                                                 u),z)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(minus,z),
                                                  app(s,x))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                 z),u)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(minus,z),
                                                  app(s,x))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(minus,
                                                                 y),x)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(minus,z),
                                                  app(s,x))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(f,
                                                                 app(s,x)),
                                                                app(app(
                                                                    minus,
                                                                    y),
                                                                 x))>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(minus,z),
                                                  app(s,x))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    f,
                                                                    app(s,x)),
                                                                 app(
                                                                  app(
                                                                   minus,
                                                                   y),
                                                                  x)),
                                                                z)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(minus,z),
                                                  app(s,x))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                 z),u)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(minus,z),
                                                  app(s,x))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(le,
                                                                 x),y)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(minus,z),
                                                  app(s,x))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(if,
                                                                 app(
                                                                  app(le,x),
                                                                  y)),
                                                                app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                                 u))>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(minus,z),
                                                  app(s,x))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                                 app(
                                                                  app(
                                                                   app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                   z),
                                                                  u)),
                                                                app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    z),
                                                                 u))>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(minus,z),
                                                  app(s,x))> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(minus,z),
                                                         app(s,x))>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(minus,z),
                                                  app(s,x))> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(f,x),u)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(minus,z),
                                                  app(s,x))> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(
                                                                    app(f,x),
                                                                    u),
                                                         app(app(minus,z),
                                                          app(s,x)))>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(minus,z),
                                                  app(s,x))> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    z),
                                                                    app(s,x))),
                                                         u)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(minus,z),
                                                  app(s,x))> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(f,x),app(s,0))>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(minus,z),
                                                  app(s,x))> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(f,x),app(s,0)),
                                           app(s,x))>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(minus,z),
                                                  app(s,x))> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(app(f,x),app(s,0)),
                                                      app(s,x)),app(s,x))>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(minus,z),
                                                  app(s,x))> 
     --> <Marked_app(app(le,app(s,x)),app(s,y)) , Marked_app(app(le,x),y)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(minus,z),
                                                  app(s,x))> 
     --> <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(f,x),u)> 
     --> <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(
                                                               app(filter,
                                                                fun),
                                                               xs)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(f,x),u)> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(filter,
                                                               fun),xs)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(f,x),u)> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(cons,
                                                               x),
                                                              app(app(
                                                                   filter,
                                                                   fun),
                                                               xs))>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(f,x),u)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(f,x),u)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(filter2,
                                                              app(fun,x)),
                                                             fun)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(f,x),u)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  filter2,
                                                                  app(fun,x)),
                                                              fun),x)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(f,x),u)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  app(
                                                                   filter2,
                                                                   app(fun,x)),
                                                                  fun),
                                                              x),xs)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(f,x),u)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    map,
                                                                    fun),
                                                          xs)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(f,x),u)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(f,x),u)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    cons,
                                                                    app(fun,x)),
                                                          app(app(map,fun),xs))>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(f,x),u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(f,
                                                                 x),u)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(f,x),u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(f,x),
                                                                 u),z)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(f,x),u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                 z),u)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(f,x),u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(minus,
                                                                 y),x)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(f,x),u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(f,
                                                                 app(s,x)),
                                                                app(app(
                                                                    minus,
                                                                    y),
                                                                 x))>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(f,x),u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    f,
                                                                    app(s,x)),
                                                                 app(
                                                                  app(
                                                                   minus,
                                                                   y),
                                                                  x)),
                                                                z)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(f,x),u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                 z),u)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(f,x),u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(le,
                                                                 x),y)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(f,x),u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(if,
                                                                 app(
                                                                  app(le,x),
                                                                  y)),
                                                                app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                                 u))>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(f,x),u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                                 app(
                                                                  app(
                                                                   app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                   z),
                                                                  u)),
                                                                app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    z),
                                                                 u))>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(f,x),u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(minus,z),
                                                         app(s,x))>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(f,x),u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(f,x),u)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(f,x),u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(
                                                                    app(f,x),
                                                                    u),
                                                         app(app(minus,z),
                                                          app(s,x)))>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(f,x),u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    z),
                                                                    app(s,x))),
                                                         u)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(f,x),u)> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(f,x),app(s,0))>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(f,x),u)> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(f,x),app(s,0)),
                                           app(s,x))>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(f,x),u)> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(app(f,x),app(s,0)),
                                                      app(s,x)),app(s,x))>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(f,x),u)> 
     --> <Marked_app(app(le,app(s,x)),app(s,y)) , Marked_app(app(le,x),y)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(f,x),u)> 
     --> <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(app(f,x),u),
                                                  app(app(minus,z),app(s,x)))> 
     --> <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(
                                                               app(filter,
                                                                fun),
                                                               xs)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(app(f,x),u),
                                                  app(app(minus,z),app(s,x)))> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(filter,
                                                               fun),xs)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(app(f,x),u),
                                                  app(app(minus,z),app(s,x)))> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(cons,
                                                               x),
                                                              app(app(
                                                                   filter,
                                                                   fun),
                                                               xs))>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(app(f,x),u),
                                                  app(app(minus,z),app(s,x)))> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(app(f,x),u),
                                                  app(app(minus,z),app(s,x)))> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(filter2,
                                                              app(fun,x)),
                                                             fun)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(app(f,x),u),
                                                  app(app(minus,z),app(s,x)))> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  filter2,
                                                                  app(fun,x)),
                                                              fun),x)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(app(f,x),u),
                                                  app(app(minus,z),app(s,x)))> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  app(
                                                                   filter2,
                                                                   app(fun,x)),
                                                                  fun),
                                                              x),xs)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(app(f,x),u),
                                                  app(app(minus,z),app(s,x)))> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    map,
                                                                    fun),
                                                          xs)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(app(f,x),u),
                                                  app(app(minus,z),app(s,x)))> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(app(f,x),u),
                                                  app(app(minus,z),app(s,x)))> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    cons,
                                                                    app(fun,x)),
                                                          app(app(map,fun),xs))>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(app(f,x),u),
                                                  app(app(minus,z),app(s,x)))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(f,
                                                                 x),u)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(app(f,x),u),
                                                  app(app(minus,z),app(s,x)))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(f,x),
                                                                 u),z)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(app(f,x),u),
                                                  app(app(minus,z),app(s,x)))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                 z),u)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(app(f,x),u),
                                                  app(app(minus,z),app(s,x)))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(minus,
                                                                 y),x)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(app(f,x),u),
                                                  app(app(minus,z),app(s,x)))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(f,
                                                                 app(s,x)),
                                                                app(app(
                                                                    minus,
                                                                    y),
                                                                 x))>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(app(f,x),u),
                                                  app(app(minus,z),app(s,x)))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    f,
                                                                    app(s,x)),
                                                                 app(
                                                                  app(
                                                                   minus,
                                                                   y),
                                                                  x)),
                                                                z)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(app(f,x),u),
                                                  app(app(minus,z),app(s,x)))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                 z),u)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(app(f,x),u),
                                                  app(app(minus,z),app(s,x)))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(le,
                                                                 x),y)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(app(f,x),u),
                                                  app(app(minus,z),app(s,x)))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(if,
                                                                 app(
                                                                  app(le,x),
                                                                  y)),
                                                                app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                                 u))>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(app(f,x),u),
                                                  app(app(minus,z),app(s,x)))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                                 app(
                                                                  app(
                                                                   app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                   z),
                                                                  u)),
                                                                app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    z),
                                                                 u))>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(app(f,x),u),
                                                  app(app(minus,z),app(s,x)))> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(minus,z),
                                                         app(s,x))>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(app(f,x),u),
                                                  app(app(minus,z),app(s,x)))> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(f,x),u)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(app(f,x),u),
                                                  app(app(minus,z),app(s,x)))> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(
                                                                    app(f,x),
                                                                    u),
                                                         app(app(minus,z),
                                                          app(s,x)))>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(app(f,x),u),
                                                  app(app(minus,z),app(s,x)))> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    z),
                                                                    app(s,x))),
                                                         u)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(app(f,x),u),
                                                  app(app(minus,z),app(s,x)))> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(f,x),app(s,0))>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(app(f,x),u),
                                                  app(app(minus,z),app(s,x)))> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(f,x),app(s,0)),
                                           app(s,x))>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(app(f,x),u),
                                                  app(app(minus,z),app(s,x)))> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(app(f,x),app(s,0)),
                                                      app(s,x)),app(s,x))>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(app(f,x),u),
                                                  app(app(minus,z),app(s,x)))> 
     --> <Marked_app(app(le,app(s,x)),app(s,y)) , Marked_app(app(le,x),y)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(app(f,x),u),
                                                  app(app(minus,z),app(s,x)))> 
     --> <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(app(app(f,x),u),
                                                             app(app(minus,z),
                                                              app(s,x))),
                                                  u)> 
     --> <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(
                                                               app(filter,
                                                                fun),
                                                               xs)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(app(app(f,x),u),
                                                             app(app(minus,z),
                                                              app(s,x))),
                                                  u)> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(filter,
                                                               fun),xs)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(app(app(f,x),u),
                                                             app(app(minus,z),
                                                              app(s,x))),
                                                  u)> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(cons,
                                                               x),
                                                              app(app(
                                                                   filter,
                                                                   fun),
                                                               xs))>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(app(app(f,x),u),
                                                             app(app(minus,z),
                                                              app(s,x))),
                                                  u)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(app(app(f,x),u),
                                                             app(app(minus,z),
                                                              app(s,x))),
                                                  u)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(filter2,
                                                              app(fun,x)),
                                                             fun)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(app(app(f,x),u),
                                                             app(app(minus,z),
                                                              app(s,x))),
                                                  u)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  filter2,
                                                                  app(fun,x)),
                                                              fun),x)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(app(app(f,x),u),
                                                             app(app(minus,z),
                                                              app(s,x))),
                                                  u)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  app(
                                                                   filter2,
                                                                   app(fun,x)),
                                                                  fun),
                                                              x),xs)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(app(app(f,x),u),
                                                             app(app(minus,z),
                                                              app(s,x))),
                                                  u)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    map,
                                                                    fun),
                                                          xs)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(app(app(f,x),u),
                                                             app(app(minus,z),
                                                              app(s,x))),
                                                  u)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(app(app(f,x),u),
                                                             app(app(minus,z),
                                                              app(s,x))),
                                                  u)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    cons,
                                                                    app(fun,x)),
                                                          app(app(map,fun),xs))>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(app(app(f,x),u),
                                                             app(app(minus,z),
                                                              app(s,x))),
                                                  u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(f,
                                                                 x),u)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(app(app(f,x),u),
                                                             app(app(minus,z),
                                                              app(s,x))),
                                                  u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(f,x),
                                                                 u),z)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(app(app(f,x),u),
                                                             app(app(minus,z),
                                                              app(s,x))),
                                                  u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                 z),u)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(app(app(f,x),u),
                                                             app(app(minus,z),
                                                              app(s,x))),
                                                  u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(minus,
                                                                 y),x)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(app(app(f,x),u),
                                                             app(app(minus,z),
                                                              app(s,x))),
                                                  u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(f,
                                                                 app(s,x)),
                                                                app(app(
                                                                    minus,
                                                                    y),
                                                                 x))>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(app(app(f,x),u),
                                                             app(app(minus,z),
                                                              app(s,x))),
                                                  u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    f,
                                                                    app(s,x)),
                                                                 app(
                                                                  app(
                                                                   minus,
                                                                   y),
                                                                  x)),
                                                                z)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(app(app(f,x),u),
                                                             app(app(minus,z),
                                                              app(s,x))),
                                                  u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                 z),u)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(app(app(f,x),u),
                                                             app(app(minus,z),
                                                              app(s,x))),
                                                  u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(le,
                                                                 x),y)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(app(app(f,x),u),
                                                             app(app(minus,z),
                                                              app(s,x))),
                                                  u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(if,
                                                                 app(
                                                                  app(le,x),
                                                                  y)),
                                                                app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                                 u))>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(app(app(f,x),u),
                                                             app(app(minus,z),
                                                              app(s,x))),
                                                  u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                                 app(
                                                                  app(
                                                                   app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                   z),
                                                                  u)),
                                                                app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    z),
                                                                 u))>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(app(app(f,x),u),
                                                             app(app(minus,z),
                                                              app(s,x))),
                                                  u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(minus,z),
                                                         app(s,x))>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(app(app(f,x),u),
                                                             app(app(minus,z),
                                                              app(s,x))),
                                                  u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(f,x),u)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(app(app(f,x),u),
                                                             app(app(minus,z),
                                                              app(s,x))),
                                                  u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(
                                                                    app(f,x),
                                                                    u),
                                                         app(app(minus,z),
                                                          app(s,x)))>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(app(app(f,x),u),
                                                             app(app(minus,z),
                                                              app(s,x))),
                                                  u)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    z),
                                                                    app(s,x))),
                                                         u)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(app(app(f,x),u),
                                                             app(app(minus,z),
                                                              app(s,x))),
                                                  u)> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(f,x),app(s,0))>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(app(app(f,x),u),
                                                             app(app(minus,z),
                                                              app(s,x))),
                                                  u)> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(f,x),app(s,0)),
                                           app(s,x))>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(app(app(f,x),u),
                                                             app(app(minus,z),
                                                              app(s,x))),
                                                  u)> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(app(f,x),app(s,0)),
                                                      app(s,x)),app(s,x))>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(app(app(f,x),u),
                                                             app(app(minus,z),
                                                              app(s,x))),
                                                  u)> 
     --> <Marked_app(app(le,app(s,x)),app(s,y)) , Marked_app(app(le,x),y)>
  <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(app(app(f,x),u),
                                                             app(app(minus,z),
                                                              app(s,x))),
                                                  u)> 
     --> <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(f,x),app(s,0))> 
     --> <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(
                                                               app(filter,
                                                                fun),
                                                               xs)>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(f,x),app(s,0))> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(filter,
                                                               fun),xs)>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(f,x),app(s,0))> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(cons,
                                                               x),
                                                              app(app(
                                                                   filter,
                                                                   fun),
                                                               xs))>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(f,x),app(s,0))> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(f,x),app(s,0))> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(filter2,
                                                              app(fun,x)),
                                                             fun)>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(f,x),app(s,0))> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  filter2,
                                                                  app(fun,x)),
                                                              fun),x)>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(f,x),app(s,0))> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  app(
                                                                   filter2,
                                                                   app(fun,x)),
                                                                  fun),
                                                              x),xs)>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(f,x),app(s,0))> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    map,
                                                                    fun),
                                                          xs)>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(f,x),app(s,0))> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(f,x),app(s,0))> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    cons,
                                                                    app(fun,x)),
                                                          app(app(map,fun),xs))>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(f,x),app(s,0))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(f,
                                                                 x),u)>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(f,x),app(s,0))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(f,x),
                                                                 u),z)>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(f,x),app(s,0))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                 z),u)>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(f,x),app(s,0))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(minus,
                                                                 y),x)>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(f,x),app(s,0))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(f,
                                                                 app(s,x)),
                                                                app(app(
                                                                    minus,
                                                                    y),
                                                                 x))>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(f,x),app(s,0))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    f,
                                                                    app(s,x)),
                                                                 app(
                                                                  app(
                                                                   minus,
                                                                   y),
                                                                  x)),
                                                                z)>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(f,x),app(s,0))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                 z),u)>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(f,x),app(s,0))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(le,
                                                                 x),y)>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(f,x),app(s,0))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(if,
                                                                 app(
                                                                  app(le,x),
                                                                  y)),
                                                                app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                                 u))>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(f,x),app(s,0))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                                 app(
                                                                  app(
                                                                   app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                   z),
                                                                  u)),
                                                                app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    z),
                                                                 u))>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(f,x),app(s,0))> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(minus,z),
                                                         app(s,x))>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(f,x),app(s,0))> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(f,x),u)>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(f,x),app(s,0))> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(
                                                                    app(f,x),
                                                                    u),
                                                         app(app(minus,z),
                                                          app(s,x)))>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(f,x),app(s,0))> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    z),
                                                                    app(s,x))),
                                                         u)>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(f,x),app(s,0))> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(f,x),app(s,0))>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(f,x),app(s,0))> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(f,x),app(s,0)),
                                           app(s,x))>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(f,x),app(s,0))> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(app(f,x),app(s,0)),
                                                      app(s,x)),app(s,x))>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(f,x),app(s,0))> 
     --> <Marked_app(app(le,app(s,x)),app(s,y)) , Marked_app(app(le,x),y)>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(f,x),app(s,0))> 
     --> <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(f,x),app(s,0)),app(s,x))> 
     --> <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(
                                                               app(filter,
                                                                fun),
                                                               xs)>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(f,x),app(s,0)),app(s,x))> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(filter,
                                                               fun),xs)>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(f,x),app(s,0)),app(s,x))> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(cons,
                                                               x),
                                                              app(app(
                                                                   filter,
                                                                   fun),
                                                               xs))>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(f,x),app(s,0)),app(s,x))> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(f,x),app(s,0)),app(s,x))> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(filter2,
                                                              app(fun,x)),
                                                             fun)>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(f,x),app(s,0)),app(s,x))> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  filter2,
                                                                  app(fun,x)),
                                                              fun),x)>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(f,x),app(s,0)),app(s,x))> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  app(
                                                                   filter2,
                                                                   app(fun,x)),
                                                                  fun),
                                                              x),xs)>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(f,x),app(s,0)),app(s,x))> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    map,
                                                                    fun),
                                                          xs)>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(f,x),app(s,0)),app(s,x))> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(f,x),app(s,0)),app(s,x))> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    cons,
                                                                    app(fun,x)),
                                                          app(app(map,fun),xs))>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(f,x),app(s,0)),app(s,x))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(f,
                                                                 x),u)>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(f,x),app(s,0)),app(s,x))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(f,x),
                                                                 u),z)>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(f,x),app(s,0)),app(s,x))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                 z),u)>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(f,x),app(s,0)),app(s,x))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(minus,
                                                                 y),x)>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(f,x),app(s,0)),app(s,x))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(f,
                                                                 app(s,x)),
                                                                app(app(
                                                                    minus,
                                                                    y),
                                                                 x))>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(f,x),app(s,0)),app(s,x))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    f,
                                                                    app(s,x)),
                                                                 app(
                                                                  app(
                                                                   minus,
                                                                   y),
                                                                  x)),
                                                                z)>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(f,x),app(s,0)),app(s,x))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                 z),u)>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(f,x),app(s,0)),app(s,x))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(le,
                                                                 x),y)>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(f,x),app(s,0)),app(s,x))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(if,
                                                                 app(
                                                                  app(le,x),
                                                                  y)),
                                                                app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                                 u))>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(f,x),app(s,0)),app(s,x))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                                 app(
                                                                  app(
                                                                   app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                   z),
                                                                  u)),
                                                                app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    z),
                                                                 u))>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(f,x),app(s,0)),app(s,x))> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(minus,z),
                                                         app(s,x))>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(f,x),app(s,0)),app(s,x))> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(f,x),u)>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(f,x),app(s,0)),app(s,x))> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(
                                                                    app(f,x),
                                                                    u),
                                                         app(app(minus,z),
                                                          app(s,x)))>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(f,x),app(s,0)),app(s,x))> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    z),
                                                                    app(s,x))),
                                                         u)>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(f,x),app(s,0)),app(s,x))> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(f,x),app(s,0))>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(f,x),app(s,0)),app(s,x))> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(f,x),app(s,0)),
                                           app(s,x))>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(f,x),app(s,0)),app(s,x))> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(app(f,x),app(s,0)),
                                                      app(s,x)),app(s,x))>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(f,x),app(s,0)),app(s,x))> 
     --> <Marked_app(app(le,app(s,x)),app(s,y)) , Marked_app(app(le,x),y)>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(f,x),app(s,0)),app(s,x))> 
     --> <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(app(f,x),app(s,0)),
                                               app(s,x)),app(s,x))> 
     --> <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(
                                                               app(filter,
                                                                fun),
                                                               xs)>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(app(f,x),app(s,0)),
                                               app(s,x)),app(s,x))> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(filter,
                                                               fun),xs)>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(app(f,x),app(s,0)),
                                               app(s,x)),app(s,x))> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(cons,
                                                               x),
                                                              app(app(
                                                                   filter,
                                                                   fun),
                                                               xs))>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(app(f,x),app(s,0)),
                                               app(s,x)),app(s,x))> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(app(f,x),app(s,0)),
                                               app(s,x)),app(s,x))> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(filter2,
                                                              app(fun,x)),
                                                             fun)>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(app(f,x),app(s,0)),
                                               app(s,x)),app(s,x))> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  filter2,
                                                                  app(fun,x)),
                                                              fun),x)>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(app(f,x),app(s,0)),
                                               app(s,x)),app(s,x))> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  app(
                                                                   filter2,
                                                                   app(fun,x)),
                                                                  fun),
                                                              x),xs)>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(app(f,x),app(s,0)),
                                               app(s,x)),app(s,x))> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    map,
                                                                    fun),
                                                          xs)>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(app(f,x),app(s,0)),
                                               app(s,x)),app(s,x))> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(app(f,x),app(s,0)),
                                               app(s,x)),app(s,x))> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    cons,
                                                                    app(fun,x)),
                                                          app(app(map,fun),xs))>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(app(f,x),app(s,0)),
                                               app(s,x)),app(s,x))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(f,
                                                                 x),u)>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(app(f,x),app(s,0)),
                                               app(s,x)),app(s,x))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(f,x),
                                                                 u),z)>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(app(f,x),app(s,0)),
                                               app(s,x)),app(s,x))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                 z),u)>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(app(f,x),app(s,0)),
                                               app(s,x)),app(s,x))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(minus,
                                                                 y),x)>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(app(f,x),app(s,0)),
                                               app(s,x)),app(s,x))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(f,
                                                                 app(s,x)),
                                                                app(app(
                                                                    minus,
                                                                    y),
                                                                 x))>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(app(f,x),app(s,0)),
                                               app(s,x)),app(s,x))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    f,
                                                                    app(s,x)),
                                                                 app(
                                                                  app(
                                                                   minus,
                                                                   y),
                                                                  x)),
                                                                z)>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(app(f,x),app(s,0)),
                                               app(s,x)),app(s,x))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                 z),u)>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(app(f,x),app(s,0)),
                                               app(s,x)),app(s,x))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(le,
                                                                 x),y)>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(app(f,x),app(s,0)),
                                               app(s,x)),app(s,x))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(if,
                                                                 app(
                                                                  app(le,x),
                                                                  y)),
                                                                app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                                 u))>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(app(f,x),app(s,0)),
                                               app(s,x)),app(s,x))> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                                 app(
                                                                  app(
                                                                   app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                   z),
                                                                  u)),
                                                                app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    z),
                                                                 u))>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(app(f,x),app(s,0)),
                                               app(s,x)),app(s,x))> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(minus,z),
                                                         app(s,x))>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(app(f,x),app(s,0)),
                                               app(s,x)),app(s,x))> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(f,x),u)>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(app(f,x),app(s,0)),
                                               app(s,x)),app(s,x))> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(
                                                                    app(f,x),
                                                                    u),
                                                         app(app(minus,z),
                                                          app(s,x)))>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(app(f,x),app(s,0)),
                                               app(s,x)),app(s,x))> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    z),
                                                                    app(s,x))),
                                                         u)>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(app(f,x),app(s,0)),
                                               app(s,x)),app(s,x))> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(f,x),app(s,0))>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(app(f,x),app(s,0)),
                                               app(s,x)),app(s,x))> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(f,x),app(s,0)),
                                           app(s,x))>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(app(f,x),app(s,0)),
                                               app(s,x)),app(s,x))> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(app(f,x),app(s,0)),
                                                      app(s,x)),app(s,x))>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(app(f,x),app(s,0)),
                                               app(s,x)),app(s,x))> 
     --> <Marked_app(app(le,app(s,x)),app(s,y)) , Marked_app(app(le,x),y)>
  <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(app(f,x),app(s,0)),
                                               app(s,x)),app(s,x))> 
     --> <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)>
  <Marked_app(app(le,app(s,x)),app(s,y)) , Marked_app(app(le,x),y)> 
     --> <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(
                                                               app(filter,
                                                                fun),
                                                               xs)>
  <Marked_app(app(le,app(s,x)),app(s,y)) , Marked_app(app(le,x),y)> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(filter,
                                                               fun),xs)>
  <Marked_app(app(le,app(s,x)),app(s,y)) , Marked_app(app(le,x),y)> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(cons,
                                                               x),
                                                              app(app(
                                                                   filter,
                                                                   fun),
                                                               xs))>
  <Marked_app(app(le,app(s,x)),app(s,y)) , Marked_app(app(le,x),y)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(le,app(s,x)),app(s,y)) , Marked_app(app(le,x),y)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(filter2,
                                                              app(fun,x)),
                                                             fun)>
  <Marked_app(app(le,app(s,x)),app(s,y)) , Marked_app(app(le,x),y)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  filter2,
                                                                  app(fun,x)),
                                                              fun),x)>
  <Marked_app(app(le,app(s,x)),app(s,y)) , Marked_app(app(le,x),y)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  app(
                                                                   filter2,
                                                                   app(fun,x)),
                                                                  fun),
                                                              x),xs)>
  <Marked_app(app(le,app(s,x)),app(s,y)) , Marked_app(app(le,x),y)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    map,
                                                                    fun),
                                                          xs)>
  <Marked_app(app(le,app(s,x)),app(s,y)) , Marked_app(app(le,x),y)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(le,app(s,x)),app(s,y)) , Marked_app(app(le,x),y)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    cons,
                                                                    app(fun,x)),
                                                          app(app(map,fun),xs))>
  <Marked_app(app(le,app(s,x)),app(s,y)) , Marked_app(app(le,x),y)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(f,
                                                                 x),u)>
  <Marked_app(app(le,app(s,x)),app(s,y)) , Marked_app(app(le,x),y)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(f,x),
                                                                 u),z)>
  <Marked_app(app(le,app(s,x)),app(s,y)) , Marked_app(app(le,x),y)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                 z),u)>
  <Marked_app(app(le,app(s,x)),app(s,y)) , Marked_app(app(le,x),y)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(minus,
                                                                 y),x)>
  <Marked_app(app(le,app(s,x)),app(s,y)) , Marked_app(app(le,x),y)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(f,
                                                                 app(s,x)),
                                                                app(app(
                                                                    minus,
                                                                    y),
                                                                 x))>
  <Marked_app(app(le,app(s,x)),app(s,y)) , Marked_app(app(le,x),y)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    f,
                                                                    app(s,x)),
                                                                 app(
                                                                  app(
                                                                   minus,
                                                                   y),
                                                                  x)),
                                                                z)>
  <Marked_app(app(le,app(s,x)),app(s,y)) , Marked_app(app(le,x),y)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                 z),u)>
  <Marked_app(app(le,app(s,x)),app(s,y)) , Marked_app(app(le,x),y)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(le,
                                                                 x),y)>
  <Marked_app(app(le,app(s,x)),app(s,y)) , Marked_app(app(le,x),y)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(if,
                                                                 app(
                                                                  app(le,x),
                                                                  y)),
                                                                app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                                 u))>
  <Marked_app(app(le,app(s,x)),app(s,y)) , Marked_app(app(le,x),y)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                                 app(
                                                                  app(
                                                                   app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                   z),
                                                                  u)),
                                                                app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    z),
                                                                 u))>
  <Marked_app(app(le,app(s,x)),app(s,y)) , Marked_app(app(le,x),y)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(minus,z),
                                                         app(s,x))>
  <Marked_app(app(le,app(s,x)),app(s,y)) , Marked_app(app(le,x),y)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(f,x),u)>
  <Marked_app(app(le,app(s,x)),app(s,y)) , Marked_app(app(le,x),y)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(
                                                                    app(f,x),
                                                                    u),
                                                         app(app(minus,z),
                                                          app(s,x)))>
  <Marked_app(app(le,app(s,x)),app(s,y)) , Marked_app(app(le,x),y)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    z),
                                                                    app(s,x))),
                                                         u)>
  <Marked_app(app(le,app(s,x)),app(s,y)) , Marked_app(app(le,x),y)> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(f,x),app(s,0))>
  <Marked_app(app(le,app(s,x)),app(s,y)) , Marked_app(app(le,x),y)> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(f,x),app(s,0)),
                                           app(s,x))>
  <Marked_app(app(le,app(s,x)),app(s,y)) , Marked_app(app(le,x),y)> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(app(f,x),app(s,0)),
                                                      app(s,x)),app(s,x))>
  <Marked_app(app(le,app(s,x)),app(s,y)) , Marked_app(app(le,x),y)> 
     --> <Marked_app(app(le,app(s,x)),app(s,y)) , Marked_app(app(le,x),y)>
  <Marked_app(app(le,app(s,x)),app(s,y)) , Marked_app(app(le,x),y)> 
     --> <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)>
  <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)> 
     --> <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(
                                                               app(filter,
                                                                fun),
                                                               xs)>
  <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(filter,
                                                               fun),xs)>
  <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(cons,
                                                               x),
                                                              app(app(
                                                                   filter,
                                                                   fun),
                                                               xs))>
  <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(filter2,
                                                              app(fun,x)),
                                                             fun)>
  <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  filter2,
                                                                  app(fun,x)),
                                                              fun),x)>
  <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  app(
                                                                   filter2,
                                                                   app(fun,x)),
                                                                  fun),
                                                              x),xs)>
  <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    map,
                                                                    fun),
                                                          xs)>
  <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    cons,
                                                                    app(fun,x)),
                                                          app(app(map,fun),xs))>
  <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(f,
                                                                 x),u)>
  <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(f,x),
                                                                 u),z)>
  <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                 z),u)>
  <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(minus,
                                                                 y),x)>
  <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(f,
                                                                 app(s,x)),
                                                                app(app(
                                                                    minus,
                                                                    y),
                                                                 x))>
  <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    f,
                                                                    app(s,x)),
                                                                 app(
                                                                  app(
                                                                   minus,
                                                                   y),
                                                                  x)),
                                                                z)>
  <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                 z),u)>
  <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(le,
                                                                 x),y)>
  <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(if,
                                                                 app(
                                                                  app(le,x),
                                                                  y)),
                                                                app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                                 u))>
  <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)> 
     --> <Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) , Marked_app(
                                                                app(app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                                 app(
                                                                  app(
                                                                   app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                   z),
                                                                  u)),
                                                                app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    z),
                                                                 u))>
  <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(minus,z),
                                                         app(s,x))>
  <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(f,x),u)>
  <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(
                                                                    app(f,x),
                                                                    u),
                                                         app(app(minus,z),
                                                          app(s,x)))>
  <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)> 
     --> <Marked_app(app(app(app(f,app(s,x)),0),z),u) , Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    z),
                                                                    app(s,x))),
                                                         u)>
  <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(f,x),app(s,0))>
  <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(f,x),app(s,0)),
                                           app(s,x))>
  <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)> 
     --> <Marked_app(perfectp,app(s,x)) , Marked_app(app(app(app(f,x),app(s,0)),
                                                      app(s,x)),app(s,x))>
  <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)> 
     --> <Marked_app(app(le,app(s,x)),app(s,y)) , Marked_app(app(le,x),y)>
  <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)> 
     --> <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  app(app(app(app(f,0),y),0),u) >= true ;
  app(app(app(app(f,0),y),app(s,z)),u) >= false ;
  app(app(app(app(f,app(s,x)),0),z),u) >= app(app(app(app(f,x),u),
                                               app(app(minus,z),app(s,x))),
                                           u) ;
  app(app(app(app(f,app(s,x)),app(s,y)),z),u) >= app(app(app(if,
                                                          app(app(le,x),y)),
                                                      app(app(app(app(
                                                                   f,
                                                                   app(s,x)),
                                                               app(app(minus,y),
                                                                x)),z),
                                                       u)),
                                                  app(app(app(app(f,x),u),z),u)) ;
  app(app(app(app(filter2,true),fun),x),xs) >= app(app(cons,x),
                                                app(app(filter,fun),xs)) ;
  app(app(app(app(filter2,false),fun),x),xs) >= app(app(filter,fun),xs) ;
  app(app(app(if,true),x),y) >= x ;
  app(app(app(if,false),x),y) >= y ;
  app(app(minus,0),y) >= 0 ;
  app(app(minus,app(s,x)),0) >= app(s,x) ;
  app(app(minus,app(s,x)),app(s,y)) >= app(app(minus,x),y) ;
  app(app(le,0),y) >= true ;
  app(app(le,app(s,x)),0) >= false ;
  app(app(le,app(s,x)),app(s,y)) >= app(app(le,x),y) ;
  app(app(map,fun),app(app(cons,x),xs)) >= app(app(cons,app(fun,x)),
                                            app(app(map,fun),xs)) ;
  app(app(map,fun),nil) >= nil ;
  app(app(filter,fun),app(app(cons,x),xs)) >= app(app(app(app(filter2,
                                                           app(fun,x)),
                                                       fun),x),xs) ;
  app(app(filter,fun),nil) >= nil ;
  app(perfectp,0) >= false ;
  app(perfectp,app(s,x)) >= app(app(app(app(f,x),app(s,0)),app(s,x)),app(s,x)) ;
  Marked_app(app(app(app(f,app(s,x)),0),z),u) >= Marked_app(app(app(app(f,x),u),
                                                             app(app(minus,z),
                                                              app(s,x))),
                                                  u) ;
  Marked_app(app(app(app(f,app(s,x)),0),z),u) >= Marked_app(app(app(f,x),u),
                                                  app(app(minus,z),app(s,x))) ;
  Marked_app(app(app(app(f,app(s,x)),0),z),u) >= Marked_app(app(minus,z),
                                                  app(s,x)) ;
  Marked_app(app(app(app(f,app(s,x)),0),z),u) >= Marked_app(app(f,x),u) ;
  Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) >= Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                         u) ;
  Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) >= Marked_app(app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    x),
                                                                    u),
                                                                    z),
                                                         u) ;
  Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) >= Marked_app(app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                                    u)),
                                                         app(app(app(
                                                                  app(f,x),
                                                                  u),
                                                              z),u)) ;
  Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) >= Marked_app(app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                         z) ;
  Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) >= Marked_app(app(
                                                                    app(f,x),
                                                                    u),
                                                         z) ;
  Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) >= Marked_app(app(minus,y),
                                                         x) ;
  Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) >= Marked_app(app(le,x),y) ;
  Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) >= Marked_app(app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                         app(app(app(
                                                                  app(
                                                                   f,
                                                                   app(s,x)),
                                                                  app(
                                                                   app(
                                                                    minus,
                                                                    y),
                                                                   x)),
                                                              z),u)) ;
  Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) >= Marked_app(app(
                                                                    f,
                                                                    app(s,x)),
                                                         app(app(minus,y),x)) ;
  Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) >= Marked_app(app(f,x),u) ;
  Marked_app(app(app(app(filter2,true),fun),x),xs) >= Marked_app(app(cons,x),
                                                       app(app(filter,fun),xs)) ;
  Marked_app(app(app(app(filter2,true),fun),x),xs) >= Marked_app(app(
                                                                  filter,
                                                                  fun),
                                                       xs) ;
  Marked_app(app(app(app(filter2,false),fun),x),xs) >= Marked_app(app(
                                                                   filter,
                                                                   fun),
                                                        xs) ;
  Marked_app(app(minus,app(s,x)),app(s,y)) >= Marked_app(app(minus,x),y) ;
  Marked_app(app(le,app(s,x)),app(s,y)) >= Marked_app(app(le,x),y) ;
  Marked_app(app(map,fun),app(app(cons,x),xs)) >= Marked_app(app(map,fun),xs) ;
  Marked_app(app(map,fun),app(app(cons,x),xs)) >= Marked_app(app(cons,
                                                              app(fun,x)),
                                                   app(app(map,fun),xs)) ;
  Marked_app(app(map,fun),app(app(cons,x),xs)) >= Marked_app(fun,x) ;
  Marked_app(app(filter,fun),app(app(cons,x),xs)) >= Marked_app(app(app(
                                                                    app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                    fun),
                                                                 x),xs) ;
  Marked_app(app(filter,fun),app(app(cons,x),xs)) >= Marked_app(app(app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                 fun),
                                                      x) ;
  Marked_app(app(filter,fun),app(app(cons,x),xs)) >= Marked_app(app(filter2,
                                                                 app(fun,x)),
                                                      fun) ;
  Marked_app(app(filter,fun),app(app(cons,x),xs)) >= Marked_app(fun,x) ;
  Marked_app(perfectp,app(s,x)) >= Marked_app(app(app(app(f,x),app(s,0)),
                                               app(s,x)),app(s,x)) ;
  Marked_app(perfectp,app(s,x)) >= Marked_app(app(app(f,x),app(s,0)),app(s,x)) ;
  Marked_app(perfectp,app(s,x)) >= Marked_app(app(f,x),app(s,0)) ;
 }
 + Disjunctions:{ 
{
  Marked_app(app(app(app(f,app(s,x)),0),z),u) > Marked_app(app(app(app(f,x),u),
                                                            app(app(minus,z),
                                                             app(s,x))),
                                                 u) ;
 }
{
  Marked_app(app(app(app(f,app(s,x)),0),z),u) > Marked_app(app(app(f,x),u),
                                                 app(app(minus,z),app(s,x))) ;
 }
{
  Marked_app(app(app(app(f,app(s,x)),0),z),u) > Marked_app(app(minus,z),
                                                 app(s,x)) ;
 }
{
  Marked_app(app(app(app(f,app(s,x)),0),z),u) > Marked_app(app(f,x),u) ;
 }
{
  Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) > Marked_app(app(
                                                                   app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                   z),
                                                        u) ;
 }
{
  Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) > Marked_app(app(
                                                                   app(
                                                                    app(f,x),
                                                                    u),
                                                                   z),
                                                        u) ;
 }
{
  Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) > Marked_app(app(
                                                                   app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                                   app(
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    f,
                                                                    app(s,x)),
                                                                    app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                                    z),
                                                                    u)),
                                                        app(app(app(app(f,x),u),
                                                             z),u)) ;
 }
{
  Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) > Marked_app(app(
                                                                   app(
                                                                    f,
                                                                    app(s,x)),
                                                                   app(
                                                                    app(
                                                                    minus,
                                                                    y),
                                                                    x)),
                                                        z) ;
 }
{
  Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) > Marked_app(app(
                                                                   app(f,x),
                                                                   u),
                                                        z) ;
 }
{
  Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) > Marked_app(app(minus,y),
                                                        x) ;
 }
{
  Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) > Marked_app(app(le,x),y) ;
 }
{
  Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) > Marked_app(app(
                                                                   if,
                                                                   app(
                                                                    app(
                                                                    le,
                                                                    x),
                                                                    y)),
                                                        app(app(app(app(
                                                                    f,
                                                                    app(s,x)),
                                                                 app(
                                                                  app(
                                                                   minus,
                                                                   y),
                                                                  x)),
                                                             z),u)) ;
 }
{
  Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) > Marked_app(app(
                                                                   f,
                                                                   app(s,x)),
                                                        app(app(minus,y),x)) ;
 }
{
  Marked_app(app(app(app(f,app(s,x)),app(s,y)),z),u) > Marked_app(app(f,x),u) ;
 }
{
  Marked_app(app(app(app(filter2,true),fun),x),xs) > Marked_app(app(cons,x),
                                                      app(app(filter,fun),xs)) ;
 }
{
  Marked_app(app(app(app(filter2,true),fun),x),xs) > Marked_app(app(filter,fun),
                                                      xs) ;
 }
{
  Marked_app(app(app(app(filter2,false),fun),x),xs) > Marked_app(app(
                                                                  filter,
                                                                  fun),
                                                       xs) ;
 }
{
  Marked_app(app(minus,app(s,x)),app(s,y)) > Marked_app(app(minus,x),y) ;
 }
{
  Marked_app(app(le,app(s,x)),app(s,y)) > Marked_app(app(le,x),y) ;
 }
{
  Marked_app(app(map,fun),app(app(cons,x),xs)) > Marked_app(app(map,fun),xs) ;
 }
{
  Marked_app(app(map,fun),app(app(cons,x),xs)) > Marked_app(app(cons,
                                                             app(fun,x)),
                                                  app(app(map,fun),xs)) ;
 }
{
  Marked_app(app(map,fun),app(app(cons,x),xs)) > Marked_app(fun,x) ;
 }
{
  Marked_app(app(filter,fun),app(app(cons,x),xs)) > Marked_app(app(app(
                                                                    app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                    fun),
                                                                x),xs) ;
 }
{
  Marked_app(app(filter,fun),app(app(cons,x),xs)) > Marked_app(app(app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                fun),
                                                     x) ;
 }
{
  Marked_app(app(filter,fun),app(app(cons,x),xs)) > Marked_app(app(filter2,
                                                                app(fun,x)),
                                                     fun) ;
 }
{
  Marked_app(app(filter,fun),app(app(cons,x),xs)) > Marked_app(fun,x) ;
 }
{
  Marked_app(perfectp,app(s,x)) > Marked_app(app(app(app(f,x),app(s,0)),
                                              app(s,x)),app(s,x)) ;
 }
{
  Marked_app(perfectp,app(s,x)) > Marked_app(app(app(f,x),app(s,0)),app(s,x)) ;
 }
{
  Marked_app(perfectp,app(s,x)) > Marked_app(app(f,x),app(s,0)) ;
 }
 } 
=== 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 : 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 : 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 : 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 : 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
=== STOPING TIMER virtual ===
Time out for these parameters.
=== TIMER virtual : 50.000000 ===
trying sub matrices of size: 1
Matrix interpretation constraints generated.
Search parameters: LINEAR MATRIX 3x3 (strict=1x1) ; time limit: 50.. 
Termination constraints generated.
Starting Sat solver initialization
=== STOPING TIMER virtual ===
No solution found for these parameters.
No solution found for these constraints.
APPLY CRITERIA (ID_CRIT)
NOT SOLVED
No proof found
Cime worked for 66.679369 seconds (real time)
Cime Exit Status: 0