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

TRS termination of:
[1] app(app(app(if,true),xs),ys) -> xs
[2] app(app(app(if,false),xs),ys) -> ys
[3] app(app(sub,x),0) -> x
[4] app(app(sub,app(s,x)),app(s,y)) -> app(app(sub,x),y)
[5] app(app(gtr,0),y) -> false
[6] app(app(gtr,app(s,x)),0) -> true
[7] app(app(gtr,app(s,x)),app(s,y)) -> app(app(gtr,x),y)
[8] app(app(d,x),0) -> true
[9] app(app(d,app(s,x)),app(s,y)) ->
 app(app(app(if,app(app(gtr,x),y)),false),
  app(app(d,app(s,x)),app(app(sub,y),x)))
[10] app(len,nil) -> 0
[11] app(len,app(app(cons,x),xs)) -> app(s,app(len,xs))
[12] app(app(filter,p),nil) -> nil
[13] app(app(filter,p),app(app(cons,x),xs)) ->
 app(app(app(if,app(p,x)),app(app(cons,x),app(app(filter,p),xs))),
  app(app(filter,p),xs))


Sub problem: 
guided: 

DP termination of:
<Marked_app(app(sub,app(s,x)),app(s,y)) , Marked_app(app(sub,x),y)>
<Marked_app(app(sub,app(s,x)),app(s,y)) , Marked_app(sub,x)>
<Marked_app(app(gtr,app(s,x)),app(s,y)) , Marked_app(app(gtr,x),y)>
<Marked_app(app(gtr,app(s,x)),app(s,y)) , Marked_app(gtr,x)>
<Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(app(if,
                                                        app(app(gtr,x),y)),
                                                    false),
                                         app(app(d,app(s,x)),app(app(sub,y),x)))>
<Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(if,app(app(gtr,x),y)),
                                         false)>
<Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(if,app(app(gtr,x),y))>
<Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(gtr,x),y)>
<Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(gtr,x)>
<Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(d,app(s,x)),
                                         app(app(sub,y),x))>
<Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(sub,y),x)>
<Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(sub,y)>
<Marked_app(len,app(app(cons,x),xs)) , Marked_app(s,app(len,xs))>
<Marked_app(len,app(app(cons,x),xs)) , Marked_app(len,xs)>
<Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(app(app(if,
                                                                 app(p,x)),
                                                             app(app(cons,x),
                                                              app(app(filter,p),
                                                               xs))),
                                                  app(app(filter,p),xs))>
<Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(app(if,app(p,x)),
                                                  app(app(cons,x),
                                                   app(app(filter,p),xs)))>
<Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(if,app(p,x))>
<Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(p,x)>
<Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(app(cons,x),
                                                  app(app(filter,p),xs))>
<Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(app(filter,p),xs)>
<Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(app(filter,p),xs)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(app(filter,p),
                                                     xs)> 
      --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(
                                                            app(filter,
                                                             p),xs)>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(app(filter,p),xs)> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(filter,
                                                            p),xs)>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(app(filter,p),xs)> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(cons,x),
                                                           app(app(filter,p),
                                                            xs))>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(app(filter,p),xs)> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(p,x)>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(app(filter,p),xs)> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(if,app(p,x)),
                                                           app(app(cons,x),
                                                            app(app(filter,p),
                                                             xs)))>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(app(filter,p),xs)> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(app(if,app(p,x)),
                                                            app(app(cons,x),
                                                             app(app(filter,p),
                                                              xs))),
                                                           app(app(filter,p),
                                                            xs))>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(app(filter,p),xs)> 
     --> <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(sub,y),x)>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(app(filter,p),xs)> 
     --> <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(d,app(s,x)),
                                                  app(app(sub,y),x))>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(app(filter,p),xs)> 
     --> <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(gtr,x),y)>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(app(filter,p),xs)> 
     --> <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(app(if,
                                                                 app(
                                                                  app(gtr,x),
                                                                  y)),
                                                             false),
                                                  app(app(d,app(s,x)),
                                                   app(app(sub,y),x)))>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(app(filter,p),xs)> 
     --> <Marked_app(app(gtr,app(s,x)),app(s,y)) , Marked_app(app(gtr,x),y)>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(app(filter,p),xs)> 
     --> <Marked_app(app(sub,app(s,x)),app(s,y)) , Marked_app(app(sub,x),y)>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(app(filter,p),xs)> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(filter,
                                                            p),xs)>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(app(filter,p),xs)> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(filter,
                                                            p),xs)>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(app(filter,p),xs)> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(cons,x),
                                                           app(app(filter,p),
                                                            xs))>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(app(filter,p),xs)> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(p,x)>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(app(filter,p),xs)> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(if,app(p,x)),
                                                           app(app(cons,x),
                                                            app(app(filter,p),
                                                             xs)))>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(app(filter,p),xs)> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(app(if,app(p,x)),
                                                            app(app(cons,x),
                                                             app(app(filter,p),
                                                              xs))),
                                                           app(app(filter,p),
                                                            xs))>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(app(filter,p),xs)> 
     --> <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(sub,y),x)>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(app(filter,p),xs)> 
     --> <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(d,app(s,x)),
                                                  app(app(sub,y),x))>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(app(filter,p),xs)> 
     --> <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(gtr,x),y)>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(app(filter,p),xs)> 
     --> <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(app(if,
                                                                 app(
                                                                  app(gtr,x),
                                                                  y)),
                                                             false),
                                                  app(app(d,app(s,x)),
                                                   app(app(sub,y),x)))>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(app(filter,p),xs)> 
     --> <Marked_app(app(gtr,app(s,x)),app(s,y)) , Marked_app(app(gtr,x),y)>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(app(filter,p),xs)> 
     --> <Marked_app(app(sub,app(s,x)),app(s,y)) , Marked_app(app(sub,x),y)>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(app(cons,x),
                                                    app(app(filter,p),xs))> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(filter,
                                                            p),xs)>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(app(cons,x),
                                                    app(app(filter,p),xs))> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(filter,
                                                            p),xs)>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(app(cons,x),
                                                    app(app(filter,p),xs))> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(cons,x),
                                                           app(app(filter,p),
                                                            xs))>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(app(cons,x),
                                                    app(app(filter,p),xs))> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(p,x)>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(app(cons,x),
                                                    app(app(filter,p),xs))> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(if,app(p,x)),
                                                           app(app(cons,x),
                                                            app(app(filter,p),
                                                             xs)))>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(app(cons,x),
                                                    app(app(filter,p),xs))> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(app(if,app(p,x)),
                                                            app(app(cons,x),
                                                             app(app(filter,p),
                                                              xs))),
                                                           app(app(filter,p),
                                                            xs))>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(app(cons,x),
                                                    app(app(filter,p),xs))> 
     --> <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(sub,y),x)>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(app(cons,x),
                                                    app(app(filter,p),xs))> 
     --> <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(d,app(s,x)),
                                                  app(app(sub,y),x))>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(app(cons,x),
                                                    app(app(filter,p),xs))> 
     --> <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(gtr,x),y)>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(app(cons,x),
                                                    app(app(filter,p),xs))> 
     --> <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(app(if,
                                                                 app(
                                                                  app(gtr,x),
                                                                  y)),
                                                             false),
                                                  app(app(d,app(s,x)),
                                                   app(app(sub,y),x)))>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(app(cons,x),
                                                    app(app(filter,p),xs))> 
     --> <Marked_app(app(gtr,app(s,x)),app(s,y)) , Marked_app(app(gtr,x),y)>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(app(cons,x),
                                                    app(app(filter,p),xs))> 
     --> <Marked_app(app(sub,app(s,x)),app(s,y)) , Marked_app(app(sub,x),y)>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(p,x)> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(filter,
                                                            p),xs)>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(p,x)> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(filter,
                                                            p),xs)>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(p,x)> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(cons,x),
                                                           app(app(filter,p),
                                                            xs))>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(p,x)> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(p,x)>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(p,x)> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(if,app(p,x)),
                                                           app(app(cons,x),
                                                            app(app(filter,p),
                                                             xs)))>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(p,x)> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(app(if,app(p,x)),
                                                            app(app(cons,x),
                                                             app(app(filter,p),
                                                              xs))),
                                                           app(app(filter,p),
                                                            xs))>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(p,x)> 
     --> <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(sub,y),x)>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(p,x)> 
     --> <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(d,app(s,x)),
                                                  app(app(sub,y),x))>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(p,x)> 
     --> <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(gtr,x),y)>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(p,x)> 
     --> <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(app(if,
                                                                 app(
                                                                  app(gtr,x),
                                                                  y)),
                                                             false),
                                                  app(app(d,app(s,x)),
                                                   app(app(sub,y),x)))>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(p,x)> 
     --> <Marked_app(app(gtr,app(s,x)),app(s,y)) , Marked_app(app(gtr,x),y)>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(p,x)> 
     --> <Marked_app(app(sub,app(s,x)),app(s,y)) , Marked_app(app(sub,x),y)>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(app(if,app(p,x)),
                                                    app(app(cons,x),
                                                     app(app(filter,p),xs)))> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(filter,
                                                            p),xs)>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(app(if,app(p,x)),
                                                    app(app(cons,x),
                                                     app(app(filter,p),xs)))> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(filter,
                                                            p),xs)>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(app(if,app(p,x)),
                                                    app(app(cons,x),
                                                     app(app(filter,p),xs)))> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(cons,x),
                                                           app(app(filter,p),
                                                            xs))>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(app(if,app(p,x)),
                                                    app(app(cons,x),
                                                     app(app(filter,p),xs)))> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(p,x)>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(app(if,app(p,x)),
                                                    app(app(cons,x),
                                                     app(app(filter,p),xs)))> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(if,app(p,x)),
                                                           app(app(cons,x),
                                                            app(app(filter,p),
                                                             xs)))>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(app(if,app(p,x)),
                                                    app(app(cons,x),
                                                     app(app(filter,p),xs)))> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(app(if,app(p,x)),
                                                            app(app(cons,x),
                                                             app(app(filter,p),
                                                              xs))),
                                                           app(app(filter,p),
                                                            xs))>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(app(if,app(p,x)),
                                                    app(app(cons,x),
                                                     app(app(filter,p),xs)))> 
     --> <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(sub,y),x)>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(app(if,app(p,x)),
                                                    app(app(cons,x),
                                                     app(app(filter,p),xs)))> 
     --> <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(d,app(s,x)),
                                                  app(app(sub,y),x))>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(app(if,app(p,x)),
                                                    app(app(cons,x),
                                                     app(app(filter,p),xs)))> 
     --> <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(gtr,x),y)>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(app(if,app(p,x)),
                                                    app(app(cons,x),
                                                     app(app(filter,p),xs)))> 
     --> <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(app(if,
                                                                 app(
                                                                  app(gtr,x),
                                                                  y)),
                                                             false),
                                                  app(app(d,app(s,x)),
                                                   app(app(sub,y),x)))>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(app(if,app(p,x)),
                                                    app(app(cons,x),
                                                     app(app(filter,p),xs)))> 
     --> <Marked_app(app(gtr,app(s,x)),app(s,y)) , Marked_app(app(gtr,x),y)>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(app(if,app(p,x)),
                                                    app(app(cons,x),
                                                     app(app(filter,p),xs)))> 
     --> <Marked_app(app(sub,app(s,x)),app(s,y)) , Marked_app(app(sub,x),y)>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                   if,
                                                                   app(p,x)),
                                                               app(app(cons,x),
                                                                app(app(
                                                                    filter,
                                                                    p),
                                                                 xs))),
                                                    app(app(filter,p),xs))> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(filter,
                                                            p),xs)>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                   if,
                                                                   app(p,x)),
                                                               app(app(cons,x),
                                                                app(app(
                                                                    filter,
                                                                    p),
                                                                 xs))),
                                                    app(app(filter,p),xs))> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(filter,
                                                            p),xs)>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                   if,
                                                                   app(p,x)),
                                                               app(app(cons,x),
                                                                app(app(
                                                                    filter,
                                                                    p),
                                                                 xs))),
                                                    app(app(filter,p),xs))> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(cons,x),
                                                           app(app(filter,p),
                                                            xs))>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                   if,
                                                                   app(p,x)),
                                                               app(app(cons,x),
                                                                app(app(
                                                                    filter,
                                                                    p),
                                                                 xs))),
                                                    app(app(filter,p),xs))> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(p,x)>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                   if,
                                                                   app(p,x)),
                                                               app(app(cons,x),
                                                                app(app(
                                                                    filter,
                                                                    p),
                                                                 xs))),
                                                    app(app(filter,p),xs))> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(if,app(p,x)),
                                                           app(app(cons,x),
                                                            app(app(filter,p),
                                                             xs)))>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                   if,
                                                                   app(p,x)),
                                                               app(app(cons,x),
                                                                app(app(
                                                                    filter,
                                                                    p),
                                                                 xs))),
                                                    app(app(filter,p),xs))> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(app(if,app(p,x)),
                                                            app(app(cons,x),
                                                             app(app(filter,p),
                                                              xs))),
                                                           app(app(filter,p),
                                                            xs))>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                   if,
                                                                   app(p,x)),
                                                               app(app(cons,x),
                                                                app(app(
                                                                    filter,
                                                                    p),
                                                                 xs))),
                                                    app(app(filter,p),xs))> 
     --> <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(sub,y),x)>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                   if,
                                                                   app(p,x)),
                                                               app(app(cons,x),
                                                                app(app(
                                                                    filter,
                                                                    p),
                                                                 xs))),
                                                    app(app(filter,p),xs))> 
     --> <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(d,app(s,x)),
                                                  app(app(sub,y),x))>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                   if,
                                                                   app(p,x)),
                                                               app(app(cons,x),
                                                                app(app(
                                                                    filter,
                                                                    p),
                                                                 xs))),
                                                    app(app(filter,p),xs))> 
     --> <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(gtr,x),y)>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                   if,
                                                                   app(p,x)),
                                                               app(app(cons,x),
                                                                app(app(
                                                                    filter,
                                                                    p),
                                                                 xs))),
                                                    app(app(filter,p),xs))> 
     --> <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(app(if,
                                                                 app(
                                                                  app(gtr,x),
                                                                  y)),
                                                             false),
                                                  app(app(d,app(s,x)),
                                                   app(app(sub,y),x)))>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                   if,
                                                                   app(p,x)),
                                                               app(app(cons,x),
                                                                app(app(
                                                                    filter,
                                                                    p),
                                                                 xs))),
                                                    app(app(filter,p),xs))> 
     --> <Marked_app(app(gtr,app(s,x)),app(s,y)) , Marked_app(app(gtr,x),y)>
  <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                   if,
                                                                   app(p,x)),
                                                               app(app(cons,x),
                                                                app(app(
                                                                    filter,
                                                                    p),
                                                                 xs))),
                                                    app(app(filter,p),xs))> 
     --> <Marked_app(app(sub,app(s,x)),app(s,y)) , Marked_app(app(sub,x),y)>
  <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(sub,y),x)> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(filter,
                                                            p),xs)>
  <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(sub,y),x)> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(filter,
                                                            p),xs)>
  <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(sub,y),x)> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(cons,x),
                                                           app(app(filter,p),
                                                            xs))>
  <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(sub,y),x)> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(p,x)>
  <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(sub,y),x)> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(if,app(p,x)),
                                                           app(app(cons,x),
                                                            app(app(filter,p),
                                                             xs)))>
  <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(sub,y),x)> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(app(if,app(p,x)),
                                                            app(app(cons,x),
                                                             app(app(filter,p),
                                                              xs))),
                                                           app(app(filter,p),
                                                            xs))>
  <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(sub,y),x)> 
     --> <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(sub,y),x)>
  <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(sub,y),x)> 
     --> <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(d,app(s,x)),
                                                  app(app(sub,y),x))>
  <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(sub,y),x)> 
     --> <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(gtr,x),y)>
  <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(sub,y),x)> 
     --> <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(app(if,
                                                                 app(
                                                                  app(gtr,x),
                                                                  y)),
                                                             false),
                                                  app(app(d,app(s,x)),
                                                   app(app(sub,y),x)))>
  <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(sub,y),x)> 
     --> <Marked_app(app(gtr,app(s,x)),app(s,y)) , Marked_app(app(gtr,x),y)>
  <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(sub,y),x)> 
     --> <Marked_app(app(sub,app(s,x)),app(s,y)) , Marked_app(app(sub,x),y)>
  <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(d,app(s,x)),
                                           app(app(sub,y),x))> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(filter,
                                                            p),xs)>
  <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(d,app(s,x)),
                                           app(app(sub,y),x))> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(filter,
                                                            p),xs)>
  <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(d,app(s,x)),
                                           app(app(sub,y),x))> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(cons,x),
                                                           app(app(filter,p),
                                                            xs))>
  <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(d,app(s,x)),
                                           app(app(sub,y),x))> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(p,x)>
  <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(d,app(s,x)),
                                           app(app(sub,y),x))> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(if,app(p,x)),
                                                           app(app(cons,x),
                                                            app(app(filter,p),
                                                             xs)))>
  <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(d,app(s,x)),
                                           app(app(sub,y),x))> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(app(if,app(p,x)),
                                                            app(app(cons,x),
                                                             app(app(filter,p),
                                                              xs))),
                                                           app(app(filter,p),
                                                            xs))>
  <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(d,app(s,x)),
                                           app(app(sub,y),x))> 
     --> <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(sub,y),x)>
  <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(d,app(s,x)),
                                           app(app(sub,y),x))> 
     --> <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(d,app(s,x)),
                                                  app(app(sub,y),x))>
  <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(d,app(s,x)),
                                           app(app(sub,y),x))> 
     --> <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(gtr,x),y)>
  <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(d,app(s,x)),
                                           app(app(sub,y),x))> 
     --> <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(app(if,
                                                                 app(
                                                                  app(gtr,x),
                                                                  y)),
                                                             false),
                                                  app(app(d,app(s,x)),
                                                   app(app(sub,y),x)))>
  <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(d,app(s,x)),
                                           app(app(sub,y),x))> 
     --> <Marked_app(app(gtr,app(s,x)),app(s,y)) , Marked_app(app(gtr,x),y)>
  <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(d,app(s,x)),
                                           app(app(sub,y),x))> 
     --> <Marked_app(app(sub,app(s,x)),app(s,y)) , Marked_app(app(sub,x),y)>
  <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(gtr,x),y)> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(filter,
                                                            p),xs)>
  <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(gtr,x),y)> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(filter,
                                                            p),xs)>
  <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(gtr,x),y)> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(cons,x),
                                                           app(app(filter,p),
                                                            xs))>
  <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(gtr,x),y)> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(p,x)>
  <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(gtr,x),y)> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(if,app(p,x)),
                                                           app(app(cons,x),
                                                            app(app(filter,p),
                                                             xs)))>
  <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(gtr,x),y)> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(app(if,app(p,x)),
                                                            app(app(cons,x),
                                                             app(app(filter,p),
                                                              xs))),
                                                           app(app(filter,p),
                                                            xs))>
  <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(gtr,x),y)> 
     --> <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(sub,y),x)>
  <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(gtr,x),y)> 
     --> <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(d,app(s,x)),
                                                  app(app(sub,y),x))>
  <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(gtr,x),y)> 
     --> <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(gtr,x),y)>
  <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(gtr,x),y)> 
     --> <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(app(if,
                                                                 app(
                                                                  app(gtr,x),
                                                                  y)),
                                                             false),
                                                  app(app(d,app(s,x)),
                                                   app(app(sub,y),x)))>
  <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(gtr,x),y)> 
     --> <Marked_app(app(gtr,app(s,x)),app(s,y)) , Marked_app(app(gtr,x),y)>
  <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(gtr,x),y)> 
     --> <Marked_app(app(sub,app(s,x)),app(s,y)) , Marked_app(app(sub,x),y)>
  <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(app(if,
                                                          app(app(gtr,x),y)),
                                                      false),
                                           app(app(d,app(s,x)),
                                            app(app(sub,y),x)))> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(filter,
                                                            p),xs)>
  <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(app(if,
                                                          app(app(gtr,x),y)),
                                                      false),
                                           app(app(d,app(s,x)),
                                            app(app(sub,y),x)))> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(filter,
                                                            p),xs)>
  <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(app(if,
                                                          app(app(gtr,x),y)),
                                                      false),
                                           app(app(d,app(s,x)),
                                            app(app(sub,y),x)))> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(cons,x),
                                                           app(app(filter,p),
                                                            xs))>
  <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(app(if,
                                                          app(app(gtr,x),y)),
                                                      false),
                                           app(app(d,app(s,x)),
                                            app(app(sub,y),x)))> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(p,x)>
  <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(app(if,
                                                          app(app(gtr,x),y)),
                                                      false),
                                           app(app(d,app(s,x)),
                                            app(app(sub,y),x)))> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(if,app(p,x)),
                                                           app(app(cons,x),
                                                            app(app(filter,p),
                                                             xs)))>
  <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(app(if,
                                                          app(app(gtr,x),y)),
                                                      false),
                                           app(app(d,app(s,x)),
                                            app(app(sub,y),x)))> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(app(if,app(p,x)),
                                                            app(app(cons,x),
                                                             app(app(filter,p),
                                                              xs))),
                                                           app(app(filter,p),
                                                            xs))>
  <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(app(if,
                                                          app(app(gtr,x),y)),
                                                      false),
                                           app(app(d,app(s,x)),
                                            app(app(sub,y),x)))> 
     --> <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(sub,y),x)>
  <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(app(if,
                                                          app(app(gtr,x),y)),
                                                      false),
                                           app(app(d,app(s,x)),
                                            app(app(sub,y),x)))> 
     --> <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(d,app(s,x)),
                                                  app(app(sub,y),x))>
  <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(app(if,
                                                          app(app(gtr,x),y)),
                                                      false),
                                           app(app(d,app(s,x)),
                                            app(app(sub,y),x)))> 
     --> <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(gtr,x),y)>
  <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(app(if,
                                                          app(app(gtr,x),y)),
                                                      false),
                                           app(app(d,app(s,x)),
                                            app(app(sub,y),x)))> 
     --> <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(app(if,
                                                                 app(
                                                                  app(gtr,x),
                                                                  y)),
                                                             false),
                                                  app(app(d,app(s,x)),
                                                   app(app(sub,y),x)))>
  <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(app(if,
                                                          app(app(gtr,x),y)),
                                                      false),
                                           app(app(d,app(s,x)),
                                            app(app(sub,y),x)))> 
     --> <Marked_app(app(gtr,app(s,x)),app(s,y)) , Marked_app(app(gtr,x),y)>
  <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(app(if,
                                                          app(app(gtr,x),y)),
                                                      false),
                                           app(app(d,app(s,x)),
                                            app(app(sub,y),x)))> 
     --> <Marked_app(app(sub,app(s,x)),app(s,y)) , Marked_app(app(sub,x),y)>
  <Marked_app(app(gtr,app(s,x)),app(s,y)) , Marked_app(app(gtr,x),y)> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(filter,
                                                            p),xs)>
  <Marked_app(app(gtr,app(s,x)),app(s,y)) , Marked_app(app(gtr,x),y)> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(filter,
                                                            p),xs)>
  <Marked_app(app(gtr,app(s,x)),app(s,y)) , Marked_app(app(gtr,x),y)> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(cons,x),
                                                           app(app(filter,p),
                                                            xs))>
  <Marked_app(app(gtr,app(s,x)),app(s,y)) , Marked_app(app(gtr,x),y)> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(p,x)>
  <Marked_app(app(gtr,app(s,x)),app(s,y)) , Marked_app(app(gtr,x),y)> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(if,app(p,x)),
                                                           app(app(cons,x),
                                                            app(app(filter,p),
                                                             xs)))>
  <Marked_app(app(gtr,app(s,x)),app(s,y)) , Marked_app(app(gtr,x),y)> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(app(if,app(p,x)),
                                                            app(app(cons,x),
                                                             app(app(filter,p),
                                                              xs))),
                                                           app(app(filter,p),
                                                            xs))>
  <Marked_app(app(gtr,app(s,x)),app(s,y)) , Marked_app(app(gtr,x),y)> 
     --> <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(sub,y),x)>
  <Marked_app(app(gtr,app(s,x)),app(s,y)) , Marked_app(app(gtr,x),y)> 
     --> <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(d,app(s,x)),
                                                  app(app(sub,y),x))>
  <Marked_app(app(gtr,app(s,x)),app(s,y)) , Marked_app(app(gtr,x),y)> 
     --> <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(gtr,x),y)>
  <Marked_app(app(gtr,app(s,x)),app(s,y)) , Marked_app(app(gtr,x),y)> 
     --> <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(app(if,
                                                                 app(
                                                                  app(gtr,x),
                                                                  y)),
                                                             false),
                                                  app(app(d,app(s,x)),
                                                   app(app(sub,y),x)))>
  <Marked_app(app(gtr,app(s,x)),app(s,y)) , Marked_app(app(gtr,x),y)> 
     --> <Marked_app(app(gtr,app(s,x)),app(s,y)) , Marked_app(app(gtr,x),y)>
  <Marked_app(app(gtr,app(s,x)),app(s,y)) , Marked_app(app(gtr,x),y)> 
     --> <Marked_app(app(sub,app(s,x)),app(s,y)) , Marked_app(app(sub,x),y)>
  <Marked_app(app(sub,app(s,x)),app(s,y)) , Marked_app(app(sub,x),y)> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(filter,
                                                            p),xs)>
  <Marked_app(app(sub,app(s,x)),app(s,y)) , Marked_app(app(sub,x),y)> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(filter,
                                                            p),xs)>
  <Marked_app(app(sub,app(s,x)),app(s,y)) , Marked_app(app(sub,x),y)> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(cons,x),
                                                           app(app(filter,p),
                                                            xs))>
  <Marked_app(app(sub,app(s,x)),app(s,y)) , Marked_app(app(sub,x),y)> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(p,x)>
  <Marked_app(app(sub,app(s,x)),app(s,y)) , Marked_app(app(sub,x),y)> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(if,app(p,x)),
                                                           app(app(cons,x),
                                                            app(app(filter,p),
                                                             xs)))>
  <Marked_app(app(sub,app(s,x)),app(s,y)) , Marked_app(app(sub,x),y)> 
     --> <Marked_app(app(filter,p),app(app(cons,x),xs)) , Marked_app(
                                                           app(app(if,app(p,x)),
                                                            app(app(cons,x),
                                                             app(app(filter,p),
                                                              xs))),
                                                           app(app(filter,p),
                                                            xs))>
  <Marked_app(app(sub,app(s,x)),app(s,y)) , Marked_app(app(sub,x),y)> 
     --> <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(sub,y),x)>
  <Marked_app(app(sub,app(s,x)),app(s,y)) , Marked_app(app(sub,x),y)> 
     --> <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(d,app(s,x)),
                                                  app(app(sub,y),x))>
  <Marked_app(app(sub,app(s,x)),app(s,y)) , Marked_app(app(sub,x),y)> 
     --> <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(gtr,x),y)>
  <Marked_app(app(sub,app(s,x)),app(s,y)) , Marked_app(app(sub,x),y)> 
     --> <Marked_app(app(d,app(s,x)),app(s,y)) , Marked_app(app(app(if,
                                                                 app(
                                                                  app(gtr,x),
                                                                  y)),
                                                             false),
                                                  app(app(d,app(s,x)),
                                                   app(app(sub,y),x)))>
  <Marked_app(app(sub,app(s,x)),app(s,y)) , Marked_app(app(sub,x),y)> 
     --> <Marked_app(app(gtr,app(s,x)),app(s,y)) , Marked_app(app(gtr,x),y)>
  <Marked_app(app(sub,app(s,x)),app(s,y)) , Marked_app(app(sub,x),y)> 
     --> <Marked_app(app(sub,app(s,x)),app(s,y)) , Marked_app(app(sub,x),y)>
}

{  <Marked_app(len,app(app(cons,x),xs)) , Marked_app(len,xs)> 
      --> <Marked_app(len,app(app(cons,x),xs)) , Marked_app(len,xs)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  app(app(app(if,true),xs),ys) >= xs ;
  app(app(app(if,false),xs),ys) >= ys ;
  app(app(sub,app(s,x)),app(s,y)) >= app(app(sub,x),y) ;
  app(app(sub,x),0) >= x ;
  app(app(gtr,app(s,x)),app(s,y)) >= app(app(gtr,x),y) ;
  app(app(gtr,app(s,x)),0) >= true ;
  app(app(gtr,0),y) >= false ;
  app(app(d,app(s,x)),app(s,y)) >= app(app(app(if,app(app(gtr,x),y)),false),
                                    app(app(d,app(s,x)),app(app(sub,y),x))) ;
  app(app(d,x),0) >= true ;
  app(app(filter,p),app(app(cons,x),xs)) >= app(app(app(if,app(p,x)),
                                                 app(app(cons,x),
                                                  app(app(filter,p),xs))),
                                             app(app(filter,p),xs)) ;
  app(app(filter,p),nil) >= nil ;
  app(len,app(app(cons,x),xs)) >= app(s,app(len,xs)) ;
  app(len,nil) >= 0 ;
  Marked_app(app(sub,app(s,x)),app(s,y)) >= Marked_app(app(sub,x),y) ;
  Marked_app(app(gtr,app(s,x)),app(s,y)) >= Marked_app(app(gtr,x),y) ;
  Marked_app(app(d,app(s,x)),app(s,y)) >= Marked_app(app(app(if,
                                                          app(app(gtr,x),y)),
                                                      false),
                                           app(app(d,app(s,x)),
                                            app(app(sub,y),x))) ;
  Marked_app(app(d,app(s,x)),app(s,y)) >= Marked_app(app(sub,y),x) ;
  Marked_app(app(d,app(s,x)),app(s,y)) >= Marked_app(app(gtr,x),y) ;
  Marked_app(app(d,app(s,x)),app(s,y)) >= Marked_app(app(d,app(s,x)),
                                           app(app(sub,y),x)) ;
  Marked_app(app(filter,p),app(app(cons,x),xs)) >= Marked_app(app(app(
                                                                   if,
                                                                   app(p,x)),
                                                               app(app(cons,x),
                                                                app(app(
                                                                    filter,
                                                                    p),
                                                                 xs))),
                                                    app(app(filter,p),xs)) ;
  Marked_app(app(filter,p),app(app(cons,x),xs)) >= Marked_app(app(if,app(p,x)),
                                                    app(app(cons,x),
                                                     app(app(filter,p),xs))) ;
  Marked_app(app(filter,p),app(app(cons,x),xs)) >= Marked_app(app(cons,x),
                                                    app(app(filter,p),xs)) ;
  Marked_app(app(filter,p),app(app(cons,x),xs)) >= Marked_app(app(filter,p),xs) ;
  Marked_app(app(filter,p),app(app(cons,x),xs)) >= Marked_app(p,x) ;
 }
 + Disjunctions:{ 
{
  Marked_app(app(sub,app(s,x)),app(s,y)) > Marked_app(app(sub,x),y) ;
 }
{
  Marked_app(app(gtr,app(s,x)),app(s,y)) > Marked_app(app(gtr,x),y) ;
 }
{
  Marked_app(app(d,app(s,x)),app(s,y)) > Marked_app(app(app(if,
                                                         app(app(gtr,x),y)),
                                                     false),
                                          app(app(d,app(s,x)),
                                           app(app(sub,y),x))) ;
 }
{
  Marked_app(app(d,app(s,x)),app(s,y)) > Marked_app(app(sub,y),x) ;
 }
{
  Marked_app(app(d,app(s,x)),app(s,y)) > Marked_app(app(gtr,x),y) ;
 }
{
  Marked_app(app(d,app(s,x)),app(s,y)) > Marked_app(app(d,app(s,x)),
                                          app(app(sub,y),x)) ;
 }
{
  Marked_app(app(filter,p),app(app(cons,x),xs)) > Marked_app(app(app(
                                                                  if,
                                                                  app(p,x)),
                                                              app(app(cons,x),
                                                               app(app(
                                                                    filter,
                                                                    p),
                                                                xs))),
                                                   app(app(filter,p),xs)) ;
 }
{
  Marked_app(app(filter,p),app(app(cons,x),xs)) > Marked_app(app(if,app(p,x)),
                                                   app(app(cons,x),
                                                    app(app(filter,p),xs))) ;
 }
{
  Marked_app(app(filter,p),app(app(cons,x),xs)) > Marked_app(app(cons,x),
                                                   app(app(filter,p),xs)) ;
 }
{
  Marked_app(app(filter,p),app(app(cons,x),xs)) > Marked_app(app(filter,p),xs) ;
 }
{
  Marked_app(app(filter,p),app(app(cons,x),xs)) > Marked_app(p,x) ;
 }
 } 
=== TIMER virtual : 10.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 10.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
Entering rpo_solver
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 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
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 50.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== 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 48.860321 seconds (real time)
Cime Exit Status: 0