- : 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(lt,app(s,x)),app(s,y)) -> app(app(lt,x),y)
[4] app(app(lt,0),app(s,y)) -> true
[5] app(app(lt,y),0) -> false
[6] app(app(eq,x),x) -> true
[7] app(app(eq,app(s,x)),0) -> false
[8] app(app(eq,0),app(s,x)) -> false
[9] app(app(merge,xs),nil) -> xs
[10] app(app(merge,nil),ys) -> ys
[11] app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) ->
 app(app(app(if,app(app(lt,x),y)),
      app(app(cons,x),app(app(merge,xs),app(app(cons,y),ys)))),
  app(app(app(if,app(app(eq,x),y)),app(app(cons,x),app(app(merge,xs),ys))),
   app(app(cons,y),app(app(merge,app(app(cons,x),xs)),ys))))
[12] app(app(map,f),nil) -> nil
[13] app(app(map,f),app(app(cons,x),xs)) ->
 app(app(cons,app(f,x)),app(app(map,f),xs))
[14] app(app(mult,0),x) -> 0
[15] app(app(mult,app(s,x)),y) -> app(app(plus,y),app(app(mult,x),y))
[16] app(app(plus,0),x) -> 0
[17] app(app(plus,app(s,x)),y) -> app(s,app(app(plus,x),y))
[18] list1 -> app(app(map,app(mult,app(s,app(s,0)))),hamming)
[19] list2 -> app(app(map,app(mult,app(s,app(s,app(s,0))))),hamming)
[20] list3 ->
 app(app(map,app(mult,app(s,app(s,app(s,app(s,app(s,0))))))),hamming)
[21] hamming ->
 app(app(cons,app(s,0)),app(app(merge,list1),app(app(merge,list2),list3)))


Sub problem: 
guided: 

DP termination of:
<Marked_app(app(lt,app(s,x)),app(s,y)) , Marked_app(app(lt,x),y)>
<Marked_app(app(lt,app(s,x)),app(s,y)) , Marked_app(lt,x)>
<Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                   app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))),
                                                                   app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))))>
<Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                   app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                   app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))))>
<Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                   if,
                                                                   app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y))>
<Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                   app(
                                                                    lt,
                                                                    x),
                                                                   y)>
<Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                   lt,
                                                                   x)>
<Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                   app(
                                                                    cons,
                                                                    x),
                                                                   app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))>
<Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                   app(
                                                                    merge,
                                                                    xs),
                                                                   app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))>
<Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                   merge,
                                                                   xs)>
<Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                   app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                   app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys)))>
<Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                   app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                   app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys)))>
<Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                   if,
                                                                   app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y))>
<Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                   app(
                                                                    eq,
                                                                    x),
                                                                   y)>
<Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                   eq,
                                                                   x)>
<Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                   app(
                                                                    cons,
                                                                    x),
                                                                   app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))>
<Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                   app(
                                                                    merge,
                                                                    xs),
                                                                   ys)>
<Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                   merge,
                                                                   xs)>
<Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                   app(
                                                                    cons,
                                                                    y),
                                                                   app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))>
<Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                   app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                   ys)>
<Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(cons,app(f,x)),
                                               app(app(map,f),xs))>
<Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(cons,app(f,x))>
<Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)>
<Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),xs)>
<Marked_app(app(mult,app(s,x)),y) , Marked_app(app(plus,y),app(app(mult,x),y))>
<Marked_app(app(mult,app(s,x)),y) , Marked_app(plus,y)>
<Marked_app(app(mult,app(s,x)),y) , Marked_app(app(mult,x),y)>
<Marked_app(app(mult,app(s,x)),y) , Marked_app(mult,x)>
<Marked_app(app(plus,app(s,x)),y) , Marked_app(s,app(app(plus,x),y))>
<Marked_app(app(plus,app(s,x)),y) , Marked_app(app(plus,x),y)>
<Marked_app(app(plus,app(s,x)),y) , Marked_app(plus,x)>
<Marked_list1 , Marked_app(app(map,app(mult,app(s,app(s,0)))),hamming)>
<Marked_list1 , Marked_app(map,app(mult,app(s,app(s,0))))>
<Marked_list1 , Marked_app(mult,app(s,app(s,0)))>
<Marked_list1 , Marked_app(s,app(s,0))>
<Marked_list1 , Marked_app(s,0)>
<Marked_list1 , Marked_hamming>
<Marked_list2 , Marked_app(app(map,app(mult,app(s,app(s,app(s,0))))),hamming)>
<Marked_list2 , Marked_app(map,app(mult,app(s,app(s,app(s,0)))))>
<Marked_list2 , Marked_app(mult,app(s,app(s,app(s,0))))>
<Marked_list2 , Marked_app(s,app(s,app(s,0)))>
<Marked_list2 , Marked_app(s,app(s,0))>
<Marked_list2 , Marked_app(s,0)>
<Marked_list2 , Marked_hamming>
<Marked_list3 , Marked_app(app(map,
                            app(mult,app(s,app(s,app(s,app(s,app(s,0))))))),
                 hamming)>
<Marked_list3 , Marked_app(map,app(mult,app(s,app(s,app(s,app(s,app(s,0)))))))>
<Marked_list3 , Marked_app(mult,app(s,app(s,app(s,app(s,app(s,0))))))>
<Marked_list3 , Marked_app(s,app(s,app(s,app(s,app(s,0)))))>
<Marked_list3 , Marked_app(s,app(s,app(s,app(s,0))))>
<Marked_list3 , Marked_app(s,app(s,app(s,0)))>
<Marked_list3 , Marked_app(s,app(s,0))>
<Marked_list3 , Marked_app(s,0)>
<Marked_list3 , Marked_hamming>
<Marked_hamming , Marked_app(app(cons,app(s,0)),
                   app(app(merge,list1),app(app(merge,list2),list3)))>
<Marked_hamming , Marked_app(cons,app(s,0))>
<Marked_hamming , Marked_app(s,0)>
<Marked_hamming , Marked_app(app(merge,list1),app(app(merge,list2),list3))>
<Marked_hamming , Marked_app(merge,list1)>
<Marked_hamming , Marked_list1>
<Marked_hamming , Marked_app(app(merge,list2),list3)>
<Marked_hamming , Marked_app(merge,list2)>
<Marked_hamming , Marked_list2>
<Marked_hamming , Marked_list3>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <Marked_hamming , Marked_list3> --> <Marked_list3 , Marked_hamming>
  <Marked_hamming , Marked_list2> --> <Marked_list2 , Marked_hamming>
  <Marked_hamming , Marked_list1> --> <Marked_list1 , Marked_hamming>
  <Marked_list3 , Marked_hamming> --> <Marked_hamming , Marked_list3>
  <Marked_list3 , Marked_hamming> --> <Marked_hamming , Marked_list2>
  <Marked_list3 , Marked_hamming> --> <Marked_hamming , Marked_list1>
  <Marked_list2 , Marked_hamming> --> <Marked_hamming , Marked_list3>
  <Marked_list2 , Marked_hamming> --> <Marked_hamming , Marked_list2>
  <Marked_list2 , Marked_hamming> --> <Marked_hamming , Marked_list1>
  <Marked_list1 , Marked_hamming> --> <Marked_hamming , Marked_list3>
  <Marked_list1 , Marked_hamming> --> <Marked_hamming , Marked_list2>
  <Marked_list1 , Marked_hamming> --> <Marked_hamming , Marked_list1>
}

{  <Marked_app(app(plus,app(s,x)),y) , Marked_app(app(plus,x),y)> 
      --> <Marked_app(app(plus,app(s,x)),y) , Marked_app(app(plus,x),y)>
  <Marked_app(app(plus,app(s,x)),y) , Marked_app(app(plus,x),y)> 
     --> <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(mult,x),y)>
  <Marked_app(app(plus,app(s,x)),y) , Marked_app(app(plus,x),y)> 
     --> <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(plus,y),
                                              app(app(mult,x),y))>
  <Marked_app(app(plus,app(s,x)),y) , Marked_app(app(plus,x),y)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),
                                                        xs)>
  <Marked_app(app(plus,app(s,x)),y) , Marked_app(app(plus,x),y)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)>
  <Marked_app(app(plus,app(s,x)),y) , Marked_app(app(plus,x),y)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                   cons,
                                                                   app(f,x)),
                                                        app(app(map,f),xs))>
  <Marked_app(app(plus,app(s,x)),y) , Marked_app(app(plus,x),y)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),ys)>
  <Marked_app(app(plus,app(s,x)),y) , Marked_app(app(plus,x),y)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))>
  <Marked_app(app(plus,app(s,x)),y) , Marked_app(app(plus,x),y)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),ys)>
  <Marked_app(app(plus,app(s,x)),y) , Marked_app(app(plus,x),y)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))>
  <Marked_app(app(plus,app(s,x)),y) , Marked_app(app(plus,x),y)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    eq,
                                                                    x),y)>
  <Marked_app(app(plus,app(s,x)),y) , Marked_app(app(plus,x),y)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys)))>
  <Marked_app(app(plus,app(s,x)),y) , Marked_app(app(plus,x),y)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys)))>
  <Marked_app(app(plus,app(s,x)),y) , Marked_app(app(plus,x),y)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))>
  <Marked_app(app(plus,app(s,x)),y) , Marked_app(app(plus,x),y)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))>
  <Marked_app(app(plus,app(s,x)),y) , Marked_app(app(plus,x),y)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    lt,
                                                                    x),y)>
  <Marked_app(app(plus,app(s,x)),y) , Marked_app(app(plus,x),y)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))))>
  <Marked_app(app(plus,app(s,x)),y) , Marked_app(app(plus,x),y)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))),
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))))>
  <Marked_app(app(plus,app(s,x)),y) , Marked_app(app(plus,x),y)> 
     --> <Marked_app(app(lt,app(s,x)),app(s,y)) , Marked_app(app(lt,x),y)>
  <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(mult,x),y)> 
     --> <Marked_app(app(plus,app(s,x)),y) , Marked_app(app(plus,x),y)>
  <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(mult,x),y)> 
     --> <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(mult,x),y)>
  <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(mult,x),y)> 
     --> <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(plus,y),
                                              app(app(mult,x),y))>
  <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(mult,x),y)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),
                                                        xs)>
  <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(mult,x),y)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)>
  <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(mult,x),y)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                   cons,
                                                                   app(f,x)),
                                                        app(app(map,f),xs))>
  <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(mult,x),y)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),ys)>
  <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(mult,x),y)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))>
  <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(mult,x),y)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),ys)>
  <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(mult,x),y)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))>
  <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(mult,x),y)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    eq,
                                                                    x),y)>
  <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(mult,x),y)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys)))>
  <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(mult,x),y)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys)))>
  <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(mult,x),y)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))>
  <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(mult,x),y)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))>
  <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(mult,x),y)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    lt,
                                                                    x),y)>
  <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(mult,x),y)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))))>
  <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(mult,x),y)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))),
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))))>
  <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(mult,x),y)> 
     --> <Marked_app(app(lt,app(s,x)),app(s,y)) , Marked_app(app(lt,x),y)>
  <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(plus,y),
                                       app(app(mult,x),y))> 
     --> <Marked_app(app(plus,app(s,x)),y) , Marked_app(app(plus,x),y)>
  <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(plus,y),
                                       app(app(mult,x),y))> 
     --> <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(mult,x),y)>
  <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(plus,y),
                                       app(app(mult,x),y))> 
     --> <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(plus,y),
                                              app(app(mult,x),y))>
  <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(plus,y),
                                       app(app(mult,x),y))> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),
                                                        xs)>
  <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(plus,y),
                                       app(app(mult,x),y))> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)>
  <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(plus,y),
                                       app(app(mult,x),y))> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                   cons,
                                                                   app(f,x)),
                                                        app(app(map,f),xs))>
  <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(plus,y),
                                       app(app(mult,x),y))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),ys)>
  <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(plus,y),
                                       app(app(mult,x),y))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))>
  <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(plus,y),
                                       app(app(mult,x),y))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),ys)>
  <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(plus,y),
                                       app(app(mult,x),y))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))>
  <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(plus,y),
                                       app(app(mult,x),y))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    eq,
                                                                    x),y)>
  <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(plus,y),
                                       app(app(mult,x),y))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys)))>
  <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(plus,y),
                                       app(app(mult,x),y))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys)))>
  <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(plus,y),
                                       app(app(mult,x),y))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))>
  <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(plus,y),
                                       app(app(mult,x),y))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))>
  <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(plus,y),
                                       app(app(mult,x),y))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    lt,
                                                                    x),y)>
  <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(plus,y),
                                       app(app(mult,x),y))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))))>
  <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(plus,y),
                                       app(app(mult,x),y))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))),
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))))>
  <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(plus,y),
                                       app(app(mult,x),y))> 
     --> <Marked_app(app(lt,app(s,x)),app(s,y)) , Marked_app(app(lt,x),y)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),xs)> 
     --> <Marked_app(app(plus,app(s,x)),y) , Marked_app(app(plus,x),y)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),xs)> 
     --> <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(mult,x),y)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),xs)> 
     --> <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(plus,y),
                                              app(app(mult,x),y))>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),xs)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),
                                                        xs)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),xs)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),xs)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                   cons,
                                                                   app(f,x)),
                                                        app(app(map,f),xs))>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),xs)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),ys)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),xs)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),xs)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),ys)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),xs)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),xs)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    eq,
                                                                    x),y)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),xs)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys)))>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),xs)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys)))>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),xs)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),xs)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),xs)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    lt,
                                                                    x),y)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),xs)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))))>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),xs)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))),
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))))>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),xs)> 
     --> <Marked_app(app(lt,app(s,x)),app(s,y)) , Marked_app(app(lt,x),y)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)> 
     --> <Marked_app(app(plus,app(s,x)),y) , Marked_app(app(plus,x),y)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)> 
     --> <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(mult,x),y)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)> 
     --> <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(plus,y),
                                              app(app(mult,x),y))>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),
                                                        xs)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                   cons,
                                                                   app(f,x)),
                                                        app(app(map,f),xs))>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),ys)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),ys)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    eq,
                                                                    x),y)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys)))>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys)))>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    lt,
                                                                    x),y)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))))>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))),
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))))>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)> 
     --> <Marked_app(app(lt,app(s,x)),app(s,y)) , Marked_app(app(lt,x),y)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(cons,app(f,x)),
                                                 app(app(map,f),xs))> 
     --> <Marked_app(app(plus,app(s,x)),y) , Marked_app(app(plus,x),y)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(cons,app(f,x)),
                                                 app(app(map,f),xs))> 
     --> <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(mult,x),y)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(cons,app(f,x)),
                                                 app(app(map,f),xs))> 
     --> <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(plus,y),
                                              app(app(mult,x),y))>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(cons,app(f,x)),
                                                 app(app(map,f),xs))> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),
                                                        xs)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(cons,app(f,x)),
                                                 app(app(map,f),xs))> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(cons,app(f,x)),
                                                 app(app(map,f),xs))> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                   cons,
                                                                   app(f,x)),
                                                        app(app(map,f),xs))>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(cons,app(f,x)),
                                                 app(app(map,f),xs))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),ys)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(cons,app(f,x)),
                                                 app(app(map,f),xs))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(cons,app(f,x)),
                                                 app(app(map,f),xs))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),ys)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(cons,app(f,x)),
                                                 app(app(map,f),xs))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(cons,app(f,x)),
                                                 app(app(map,f),xs))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    eq,
                                                                    x),y)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(cons,app(f,x)),
                                                 app(app(map,f),xs))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys)))>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(cons,app(f,x)),
                                                 app(app(map,f),xs))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys)))>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(cons,app(f,x)),
                                                 app(app(map,f),xs))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(cons,app(f,x)),
                                                 app(app(map,f),xs))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(cons,app(f,x)),
                                                 app(app(map,f),xs))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    lt,
                                                                    x),y)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(cons,app(f,x)),
                                                 app(app(map,f),xs))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))))>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(cons,app(f,x)),
                                                 app(app(map,f),xs))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))),
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))))>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(cons,app(f,x)),
                                                 app(app(map,f),xs))> 
     --> <Marked_app(app(lt,app(s,x)),app(s,y)) , Marked_app(app(lt,x),y)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys)> 
     --> <Marked_app(app(plus,app(s,x)),y) , Marked_app(app(plus,x),y)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys)> 
     --> <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(mult,x),y)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys)> 
     --> <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(plus,y),
                                              app(app(mult,x),y))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),
                                                        xs)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                   cons,
                                                                   app(f,x)),
                                                        app(app(map,f),xs))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),ys)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),ys)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    eq,
                                                                    x),y)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys)))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys)))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    lt,
                                                                    x),y)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))),
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys)> 
     --> <Marked_app(app(lt,app(s,x)),app(s,y)) , Marked_app(app(lt,x),y)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))> 
     --> <Marked_app(app(plus,app(s,x)),y) , Marked_app(app(plus,x),y)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))> 
     --> <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(mult,x),y)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))> 
     --> <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(plus,y),
                                              app(app(mult,x),y))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),
                                                        xs)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                   cons,
                                                                   app(f,x)),
                                                        app(app(map,f),xs))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),ys)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),ys)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    eq,
                                                                    x),y)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys)))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys)))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    lt,
                                                                    x),y)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))),
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))> 
     --> <Marked_app(app(lt,app(s,x)),app(s,y)) , Marked_app(app(lt,x),y)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys)> 
     --> <Marked_app(app(plus,app(s,x)),y) , Marked_app(app(plus,x),y)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys)> 
     --> <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(mult,x),y)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys)> 
     --> <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(plus,y),
                                              app(app(mult,x),y))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),
                                                        xs)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                   cons,
                                                                   app(f,x)),
                                                        app(app(map,f),xs))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),ys)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),ys)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    eq,
                                                                    x),y)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys)))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys)))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    lt,
                                                                    x),y)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))),
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys)> 
     --> <Marked_app(app(lt,app(s,x)),app(s,y)) , Marked_app(app(lt,x),y)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))> 
     --> <Marked_app(app(plus,app(s,x)),y) , Marked_app(app(plus,x),y)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))> 
     --> <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(mult,x),y)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))> 
     --> <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(plus,y),
                                              app(app(mult,x),y))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),
                                                        xs)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                   cons,
                                                                   app(f,x)),
                                                        app(app(map,f),xs))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),ys)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),ys)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    eq,
                                                                    x),y)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys)))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys)))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    lt,
                                                                    x),y)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))),
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))> 
     --> <Marked_app(app(lt,app(s,x)),app(s,y)) , Marked_app(app(lt,x),y)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)> 
     --> <Marked_app(app(plus,app(s,x)),y) , Marked_app(app(plus,x),y)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)> 
     --> <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(mult,x),y)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)> 
     --> <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(plus,y),
                                              app(app(mult,x),y))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),
                                                        xs)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                   cons,
                                                                   app(f,x)),
                                                        app(app(map,f),xs))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),ys)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),ys)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    eq,
                                                                    x),y)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys)))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys)))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    lt,
                                                                    x),y)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))),
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)> 
     --> <Marked_app(app(lt,app(s,x)),app(s,y)) , Marked_app(app(lt,x),y)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys)))> 
     --> <Marked_app(app(plus,app(s,x)),y) , Marked_app(app(plus,x),y)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys)))> 
     --> <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(mult,x),y)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys)))> 
     --> <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(plus,y),
                                              app(app(mult,x),y))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys)))> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),
                                                        xs)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys)))> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys)))> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                   cons,
                                                                   app(f,x)),
                                                        app(app(map,f),xs))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys)))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),ys)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys)))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys)))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),ys)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys)))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys)))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    eq,
                                                                    x),y)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys)))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys)))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys)))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys)))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys)))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys)))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys)))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    lt,
                                                                    x),y)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys)))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys)))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))),
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys)))> 
     --> <Marked_app(app(lt,app(s,x)),app(s,y)) , Marked_app(app(lt,x),y)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys)))> 
     --> <Marked_app(app(plus,app(s,x)),y) , Marked_app(app(plus,x),y)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys)))> 
     --> <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(mult,x),y)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys)))> 
     --> <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(plus,y),
                                              app(app(mult,x),y))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys)))> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),
                                                        xs)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys)))> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys)))> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                   cons,
                                                                   app(f,x)),
                                                        app(app(map,f),xs))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys)))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),ys)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys)))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys)))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),ys)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys)))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys)))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    eq,
                                                                    x),y)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys)))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys)))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys)))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys)))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys)))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys)))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys)))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    lt,
                                                                    x),y)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys)))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys)))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))),
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys)))> 
     --> <Marked_app(app(lt,app(s,x)),app(s,y)) , Marked_app(app(lt,x),y)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))> 
     --> <Marked_app(app(plus,app(s,x)),y) , Marked_app(app(plus,x),y)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))> 
     --> <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(mult,x),y)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))> 
     --> <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(plus,y),
                                              app(app(mult,x),y))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),
                                                        xs)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                   cons,
                                                                   app(f,x)),
                                                        app(app(map,f),xs))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),ys)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),ys)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    eq,
                                                                    x),y)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys)))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys)))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    lt,
                                                                    x),y)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))),
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))> 
     --> <Marked_app(app(lt,app(s,x)),app(s,y)) , Marked_app(app(lt,x),y)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))> 
     --> <Marked_app(app(plus,app(s,x)),y) , Marked_app(app(plus,x),y)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))> 
     --> <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(mult,x),y)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))> 
     --> <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(plus,y),
                                              app(app(mult,x),y))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),
                                                        xs)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                   cons,
                                                                   app(f,x)),
                                                        app(app(map,f),xs))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),ys)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),ys)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    eq,
                                                                    x),y)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys)))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys)))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    lt,
                                                                    x),y)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))),
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))> 
     --> <Marked_app(app(lt,app(s,x)),app(s,y)) , Marked_app(app(lt,x),y)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)> 
     --> <Marked_app(app(plus,app(s,x)),y) , Marked_app(app(plus,x),y)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)> 
     --> <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(mult,x),y)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)> 
     --> <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(plus,y),
                                              app(app(mult,x),y))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),
                                                        xs)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                   cons,
                                                                   app(f,x)),
                                                        app(app(map,f),xs))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),ys)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),ys)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    eq,
                                                                    x),y)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys)))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys)))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    lt,
                                                                    x),y)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))),
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)> 
     --> <Marked_app(app(lt,app(s,x)),app(s,y)) , Marked_app(app(lt,x),y)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))))> 
     --> <Marked_app(app(plus,app(s,x)),y) , Marked_app(app(plus,x),y)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))))> 
     --> <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(mult,x),y)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))))> 
     --> <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(plus,y),
                                              app(app(mult,x),y))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))))> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),
                                                        xs)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))))> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))))> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                   cons,
                                                                   app(f,x)),
                                                        app(app(map,f),xs))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),ys)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),ys)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    eq,
                                                                    x),y)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys)))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys)))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    lt,
                                                                    x),y)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))),
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))))> 
     --> <Marked_app(app(lt,app(s,x)),app(s,y)) , Marked_app(app(lt,x),y)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))),
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))))> 
     --> <Marked_app(app(plus,app(s,x)),y) , Marked_app(app(plus,x),y)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))),
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))))> 
     --> <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(mult,x),y)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))),
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))))> 
     --> <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(plus,y),
                                              app(app(mult,x),y))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))),
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))))> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),
                                                        xs)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))),
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))))> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))),
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))))> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                   cons,
                                                                   app(f,x)),
                                                        app(app(map,f),xs))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))),
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),ys)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))),
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))),
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),ys)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))),
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))),
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    eq,
                                                                    x),y)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))),
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys)))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))),
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys)))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))),
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))),
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))),
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    lt,
                                                                    x),y)>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))),
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))),
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))))> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))),
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))))>
  <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))),
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))))> 
     --> <Marked_app(app(lt,app(s,x)),app(s,y)) , Marked_app(app(lt,x),y)>
  <Marked_app(app(lt,app(s,x)),app(s,y)) , Marked_app(app(lt,x),y)> 
     --> <Marked_app(app(plus,app(s,x)),y) , Marked_app(app(plus,x),y)>
  <Marked_app(app(lt,app(s,x)),app(s,y)) , Marked_app(app(lt,x),y)> 
     --> <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(mult,x),y)>
  <Marked_app(app(lt,app(s,x)),app(s,y)) , Marked_app(app(lt,x),y)> 
     --> <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(plus,y),
                                              app(app(mult,x),y))>
  <Marked_app(app(lt,app(s,x)),app(s,y)) , Marked_app(app(lt,x),y)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),
                                                        xs)>
  <Marked_app(app(lt,app(s,x)),app(s,y)) , Marked_app(app(lt,x),y)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)>
  <Marked_app(app(lt,app(s,x)),app(s,y)) , Marked_app(app(lt,x),y)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                   cons,
                                                                   app(f,x)),
                                                        app(app(map,f),xs))>
  <Marked_app(app(lt,app(s,x)),app(s,y)) , Marked_app(app(lt,x),y)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),ys)>
  <Marked_app(app(lt,app(s,x)),app(s,y)) , Marked_app(app(lt,x),y)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))>
  <Marked_app(app(lt,app(s,x)),app(s,y)) , Marked_app(app(lt,x),y)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),ys)>
  <Marked_app(app(lt,app(s,x)),app(s,y)) , Marked_app(app(lt,x),y)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))>
  <Marked_app(app(lt,app(s,x)),app(s,y)) , Marked_app(app(lt,x),y)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    eq,
                                                                    x),y)>
  <Marked_app(app(lt,app(s,x)),app(s,y)) , Marked_app(app(lt,x),y)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys)))>
  <Marked_app(app(lt,app(s,x)),app(s,y)) , Marked_app(app(lt,x),y)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys)))>
  <Marked_app(app(lt,app(s,x)),app(s,y)) , Marked_app(app(lt,x),y)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))>
  <Marked_app(app(lt,app(s,x)),app(s,y)) , Marked_app(app(lt,x),y)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))>
  <Marked_app(app(lt,app(s,x)),app(s,y)) , Marked_app(app(lt,x),y)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    lt,
                                                                    x),y)>
  <Marked_app(app(lt,app(s,x)),app(s,y)) , Marked_app(app(lt,x),y)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys))))>
  <Marked_app(app(lt,app(s,x)),app(s,y)) , Marked_app(app(lt,x),y)> 
     --> <Marked_app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) , Marked_app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))),
                                                                    app(
                                                                    app(
                                                                    app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                    ys))))>
  <Marked_app(app(lt,app(s,x)),app(s,y)) , Marked_app(app(lt,x),y)> 
     --> <Marked_app(app(lt,app(s,x)),app(s,y)) , Marked_app(app(lt,x),y)>
}
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(lt,app(s,x)),app(s,y)) >= app(app(lt,x),y) ;
  app(app(lt,0),app(s,y)) >= true ;
  app(app(lt,y),0) >= false ;
  app(app(eq,app(s,x)),0) >= false ;
  app(app(eq,0),app(s,x)) >= false ;
  app(app(eq,x),x) >= true ;
  app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) >= app(app(
                                                                  app(
                                                                   if,
                                                                   app(
                                                                    app(
                                                                    lt,
                                                                    x),
                                                                    y)),
                                                                  app(
                                                                   app(
                                                                    cons,
                                                                    x),
                                                                   app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    y),
                                                                    ys)))),
                                                              app(app(
                                                                   app(
                                                                    if,
                                                                    app(
                                                                    app(
                                                                    eq,
                                                                    x),
                                                                    y)),
                                                                   app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    app(
                                                                    app(
                                                                    merge,
                                                                    xs),
                                                                    ys))),
                                                               app(app(cons,y),
                                                                app(app(
                                                                    merge,
                                                                    app(
                                                                    app(
                                                                    cons,
                                                                    x),
                                                                    xs)),
                                                                 ys)))) ;
  app(app(merge,nil),ys) >= ys ;
  app(app(merge,xs),nil) >= xs ;
  app(app(map,f),app(app(cons,x),xs)) >= app(app(cons,app(f,x)),
                                          app(app(map,f),xs)) ;
  app(app(map,f),nil) >= nil ;
  app(app(mult,app(s,x)),y) >= app(app(plus,y),app(app(mult,x),y)) ;
  app(app(mult,0),x) >= 0 ;
  app(app(plus,app(s,x)),y) >= app(s,app(app(plus,x),y)) ;
  app(app(plus,0),x) >= 0 ;
  hamming >= app(app(cons,app(s,0)),
              app(app(merge,list1),app(app(merge,list2),list3))) ;
  list1 >= app(app(map,app(mult,app(s,app(s,0)))),hamming) ;
  list2 >= app(app(map,app(mult,app(s,app(s,app(s,0))))),hamming) ;
  list3 >= app(app(map,app(mult,app(s,app(s,app(s,app(s,app(s,0))))))),hamming) ;
  Marked_hamming >= Marked_list1 ;
  Marked_hamming >= Marked_list2 ;
  Marked_hamming >= Marked_list3 ;
  Marked_list1 >= Marked_hamming ;
  Marked_list2 >= Marked_hamming ;
  Marked_list3 >= Marked_hamming ;
 }
 + Disjunctions:{ 
{
  Marked_hamming > Marked_list1 ;
 }
{
  Marked_hamming > Marked_list2 ;
 }
{
  Marked_hamming > Marked_list3 ;
 }
{
  Marked_list1 > Marked_hamming ;
 }
{
  Marked_list2 > Marked_hamming ;
 }
{
  Marked_list3 > Marked_hamming ;
 }
 } 
=== 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 : 15.000000 ===
Entering poly_solver
=== 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 66.052111 seconds (real time)
Cime Exit Status: 0