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

TRS termination of:
[1] active(natsFrom(N)) -> mark(cons(N,natsFrom(s(N))))
[2] active(fst(pair(XS,YS))) -> mark(XS)
[3] active(snd(pair(XS,YS))) -> mark(YS)
[4] active(splitAt(0,XS)) -> mark(pair(nil,XS))
[5] active(splitAt(s(N),cons(X,XS))) -> mark(u(splitAt(N,XS),N,X,XS))
[6] active(u(pair(YS,ZS),N,X,XS)) -> mark(pair(cons(X,YS),ZS))
[7] active(head(cons(N,XS))) -> mark(N)
[8] active(tail(cons(N,XS))) -> mark(XS)
[9] active(sel(N,XS)) -> mark(head(afterNth(N,XS)))
[10] active(take(N,XS)) -> mark(fst(splitAt(N,XS)))
[11] active(afterNth(N,XS)) -> mark(snd(splitAt(N,XS)))
[12] active(natsFrom(X)) -> natsFrom(active(X))
[13] active(cons(X1,X2)) -> cons(active(X1),X2)
[14] active(s(X)) -> s(active(X))
[15] active(fst(X)) -> fst(active(X))
[16] active(pair(X1,X2)) -> pair(active(X1),X2)
[17] active(pair(X1,X2)) -> pair(X1,active(X2))
[18] active(snd(X)) -> snd(active(X))
[19] active(splitAt(X1,X2)) -> splitAt(active(X1),X2)
[20] active(splitAt(X1,X2)) -> splitAt(X1,active(X2))
[21] active(u(X1,X2,X3,X4)) -> u(active(X1),X2,X3,X4)
[22] active(head(X)) -> head(active(X))
[23] active(tail(X)) -> tail(active(X))
[24] active(sel(X1,X2)) -> sel(active(X1),X2)
[25] active(sel(X1,X2)) -> sel(X1,active(X2))
[26] active(afterNth(X1,X2)) -> afterNth(active(X1),X2)
[27] active(afterNth(X1,X2)) -> afterNth(X1,active(X2))
[28] active(take(X1,X2)) -> take(active(X1),X2)
[29] active(take(X1,X2)) -> take(X1,active(X2))
[30] natsFrom(mark(X)) -> mark(natsFrom(X))
[31] cons(mark(X1),X2) -> mark(cons(X1,X2))
[32] s(mark(X)) -> mark(s(X))
[33] fst(mark(X)) -> mark(fst(X))
[34] pair(mark(X1),X2) -> mark(pair(X1,X2))
[35] pair(X1,mark(X2)) -> mark(pair(X1,X2))
[36] snd(mark(X)) -> mark(snd(X))
[37] splitAt(mark(X1),X2) -> mark(splitAt(X1,X2))
[38] splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2))
[39] u(mark(X1),X2,X3,X4) -> mark(u(X1,X2,X3,X4))
[40] head(mark(X)) -> mark(head(X))
[41] tail(mark(X)) -> mark(tail(X))
[42] sel(mark(X1),X2) -> mark(sel(X1,X2))
[43] sel(X1,mark(X2)) -> mark(sel(X1,X2))
[44] afterNth(mark(X1),X2) -> mark(afterNth(X1,X2))
[45] afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2))
[46] take(mark(X1),X2) -> mark(take(X1,X2))
[47] take(X1,mark(X2)) -> mark(take(X1,X2))
[48] proper(natsFrom(X)) -> natsFrom(proper(X))
[49] proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
[50] proper(s(X)) -> s(proper(X))
[51] proper(fst(X)) -> fst(proper(X))
[52] proper(pair(X1,X2)) -> pair(proper(X1),proper(X2))
[53] proper(snd(X)) -> snd(proper(X))
[54] proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2))
[55] proper(0) -> ok(0)
[56] proper(nil) -> ok(nil)
[57] proper(u(X1,X2,X3,X4)) -> u(proper(X1),proper(X2),proper(X3),proper(X4))
[58] proper(head(X)) -> head(proper(X))
[59] proper(tail(X)) -> tail(proper(X))
[60] proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
[61] proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2))
[62] proper(take(X1,X2)) -> take(proper(X1),proper(X2))
[63] natsFrom(ok(X)) -> ok(natsFrom(X))
[64] cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
[65] s(ok(X)) -> ok(s(X))
[66] fst(ok(X)) -> ok(fst(X))
[67] pair(ok(X1),ok(X2)) -> ok(pair(X1,X2))
[68] snd(ok(X)) -> ok(snd(X))
[69] splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2))
[70] u(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(u(X1,X2,X3,X4))
[71] head(ok(X)) -> ok(head(X))
[72] tail(ok(X)) -> ok(tail(X))
[73] sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
[74] afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2))
[75] take(ok(X1),ok(X2)) -> ok(take(X1,X2))
[76] top(mark(X)) -> top(proper(X))
[77] top(ok(X)) -> top(active(X))


Sub problem: 
guided: 

DP termination of:
<Marked_active(natsFrom(N)) , Marked_cons(N,natsFrom(s(N)))>
<Marked_active(natsFrom(N)) , Marked_natsFrom(s(N))>
<Marked_active(natsFrom(N)) , Marked_s(N)>
<Marked_active(splitAt(0,XS)) , Marked_pair(nil,XS)>
<Marked_active(splitAt(s(N),cons(X,XS))) , Marked_u(splitAt(N,XS),N,X,XS)>
<Marked_active(splitAt(s(N),cons(X,XS))) , Marked_splitAt(N,XS)>
<Marked_active(u(pair(YS,ZS),N,X,XS)) , Marked_pair(cons(X,YS),ZS)>
<Marked_active(u(pair(YS,ZS),N,X,XS)) , Marked_cons(X,YS)>
<Marked_active(sel(N,XS)) , Marked_head(afterNth(N,XS))>
<Marked_active(sel(N,XS)) , Marked_afterNth(N,XS)>
<Marked_active(take(N,XS)) , Marked_fst(splitAt(N,XS))>
<Marked_active(take(N,XS)) , Marked_splitAt(N,XS)>
<Marked_active(afterNth(N,XS)) , Marked_snd(splitAt(N,XS))>
<Marked_active(afterNth(N,XS)) , Marked_splitAt(N,XS)>
<Marked_active(natsFrom(X)) , Marked_natsFrom(active(X))>
<Marked_active(natsFrom(X)) , Marked_active(X)>
<Marked_active(cons(X1,X2)) , Marked_cons(active(X1),X2)>
<Marked_active(cons(X1,X2)) , Marked_active(X1)>
<Marked_active(s(X)) , Marked_s(active(X))>
<Marked_active(s(X)) , Marked_active(X)>
<Marked_active(fst(X)) , Marked_fst(active(X))>
<Marked_active(fst(X)) , Marked_active(X)>
<Marked_active(pair(X1,X2)) , Marked_pair(active(X1),X2)>
<Marked_active(pair(X1,X2)) , Marked_active(X1)>
<Marked_active(pair(X1,X2)) , Marked_pair(X1,active(X2))>
<Marked_active(pair(X1,X2)) , Marked_active(X2)>
<Marked_active(snd(X)) , Marked_snd(active(X))>
<Marked_active(snd(X)) , Marked_active(X)>
<Marked_active(splitAt(X1,X2)) , Marked_splitAt(active(X1),X2)>
<Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
<Marked_active(splitAt(X1,X2)) , Marked_splitAt(X1,active(X2))>
<Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
<Marked_active(u(X1,X2,X3,X4)) , Marked_u(active(X1),X2,X3,X4)>
<Marked_active(u(X1,X2,X3,X4)) , Marked_active(X1)>
<Marked_active(head(X)) , Marked_head(active(X))>
<Marked_active(head(X)) , Marked_active(X)>
<Marked_active(tail(X)) , Marked_tail(active(X))>
<Marked_active(tail(X)) , Marked_active(X)>
<Marked_active(sel(X1,X2)) , Marked_sel(active(X1),X2)>
<Marked_active(sel(X1,X2)) , Marked_active(X1)>
<Marked_active(sel(X1,X2)) , Marked_sel(X1,active(X2))>
<Marked_active(sel(X1,X2)) , Marked_active(X2)>
<Marked_active(afterNth(X1,X2)) , Marked_afterNth(active(X1),X2)>
<Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
<Marked_active(afterNth(X1,X2)) , Marked_afterNth(X1,active(X2))>
<Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
<Marked_active(take(X1,X2)) , Marked_take(active(X1),X2)>
<Marked_active(take(X1,X2)) , Marked_active(X1)>
<Marked_active(take(X1,X2)) , Marked_take(X1,active(X2))>
<Marked_active(take(X1,X2)) , Marked_active(X2)>
<Marked_natsFrom(mark(X)) , Marked_natsFrom(X)>
<Marked_cons(mark(X1),X2) , Marked_cons(X1,X2)>
<Marked_s(mark(X)) , Marked_s(X)>
<Marked_fst(mark(X)) , Marked_fst(X)>
<Marked_pair(mark(X1),X2) , Marked_pair(X1,X2)>
<Marked_pair(X1,mark(X2)) , Marked_pair(X1,X2)>
<Marked_snd(mark(X)) , Marked_snd(X)>
<Marked_splitAt(mark(X1),X2) , Marked_splitAt(X1,X2)>
<Marked_splitAt(X1,mark(X2)) , Marked_splitAt(X1,X2)>
<Marked_u(mark(X1),X2,X3,X4) , Marked_u(X1,X2,X3,X4)>
<Marked_head(mark(X)) , Marked_head(X)>
<Marked_tail(mark(X)) , Marked_tail(X)>
<Marked_sel(mark(X1),X2) , Marked_sel(X1,X2)>
<Marked_sel(X1,mark(X2)) , Marked_sel(X1,X2)>
<Marked_afterNth(mark(X1),X2) , Marked_afterNth(X1,X2)>
<Marked_afterNth(X1,mark(X2)) , Marked_afterNth(X1,X2)>
<Marked_take(mark(X1),X2) , Marked_take(X1,X2)>
<Marked_take(X1,mark(X2)) , Marked_take(X1,X2)>
<Marked_proper(natsFrom(X)) , Marked_natsFrom(proper(X))>
<Marked_proper(natsFrom(X)) , Marked_proper(X)>
<Marked_proper(cons(X1,X2)) , Marked_cons(proper(X1),proper(X2))>
<Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
<Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
<Marked_proper(s(X)) , Marked_s(proper(X))>
<Marked_proper(s(X)) , Marked_proper(X)>
<Marked_proper(fst(X)) , Marked_fst(proper(X))>
<Marked_proper(fst(X)) , Marked_proper(X)>
<Marked_proper(pair(X1,X2)) , Marked_pair(proper(X1),proper(X2))>
<Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
<Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
<Marked_proper(snd(X)) , Marked_snd(proper(X))>
<Marked_proper(snd(X)) , Marked_proper(X)>
<Marked_proper(splitAt(X1,X2)) , Marked_splitAt(proper(X1),proper(X2))>
<Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
<Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
<Marked_proper(u(X1,X2,X3,X4)) , Marked_u(proper(X1),proper(X2),proper(X3),
                                  proper(X4))>
<Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X1)>
<Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X2)>
<Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X3)>
<Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X4)>
<Marked_proper(head(X)) , Marked_head(proper(X))>
<Marked_proper(head(X)) , Marked_proper(X)>
<Marked_proper(tail(X)) , Marked_tail(proper(X))>
<Marked_proper(tail(X)) , Marked_proper(X)>
<Marked_proper(sel(X1,X2)) , Marked_sel(proper(X1),proper(X2))>
<Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
<Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
<Marked_proper(afterNth(X1,X2)) , Marked_afterNth(proper(X1),proper(X2))>
<Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
<Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
<Marked_proper(take(X1,X2)) , Marked_take(proper(X1),proper(X2))>
<Marked_proper(take(X1,X2)) , Marked_proper(X1)>
<Marked_proper(take(X1,X2)) , Marked_proper(X2)>
<Marked_natsFrom(ok(X)) , Marked_natsFrom(X)>
<Marked_cons(ok(X1),ok(X2)) , Marked_cons(X1,X2)>
<Marked_s(ok(X)) , Marked_s(X)>
<Marked_fst(ok(X)) , Marked_fst(X)>
<Marked_pair(ok(X1),ok(X2)) , Marked_pair(X1,X2)>
<Marked_snd(ok(X)) , Marked_snd(X)>
<Marked_splitAt(ok(X1),ok(X2)) , Marked_splitAt(X1,X2)>
<Marked_u(ok(X1),ok(X2),ok(X3),ok(X4)) , Marked_u(X1,X2,X3,X4)>
<Marked_head(ok(X)) , Marked_head(X)>
<Marked_tail(ok(X)) , Marked_tail(X)>
<Marked_sel(ok(X1),ok(X2)) , Marked_sel(X1,X2)>
<Marked_afterNth(ok(X1),ok(X2)) , Marked_afterNth(X1,X2)>
<Marked_take(ok(X1),ok(X2)) , Marked_take(X1,X2)>
<Marked_top(mark(X)) , Marked_top(proper(X))>
<Marked_top(mark(X)) , Marked_proper(X)>
<Marked_top(ok(X)) , Marked_top(active(X))>
<Marked_top(ok(X)) , Marked_active(X)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 16 components:

{  <Marked_top(ok(X)) , Marked_top(active(X))> 
      --> <Marked_top(ok(X)) , Marked_top(active(X))>
  <Marked_top(ok(X)) , Marked_top(active(X))> 
     --> <Marked_top(mark(X)) , Marked_top(proper(X))>
  <Marked_top(mark(X)) , Marked_top(proper(X))> 
     --> <Marked_top(ok(X)) , Marked_top(active(X))>
  <Marked_top(mark(X)) , Marked_top(proper(X))> 
     --> <Marked_top(mark(X)) , Marked_top(proper(X))>
}

{  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
      --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(take(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(sel(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(head(X)) , Marked_proper(X)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X4)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X3)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(snd(X)) , Marked_proper(X)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(pair(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(fst(X)) , Marked_proper(X)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(take(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(afterNth(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(sel(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(head(X)) , Marked_proper(X)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X4)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X3)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(u(X1,X2,X3,X4)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(splitAt(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(snd(X)) , Marked_proper(X)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(pair(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(fst(X)) , Marked_proper(X)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(natsFrom(X)) , Marked_proper(X)> 
     --> <Marked_proper(natsFrom(X)) , Marked_proper(X)>
}

{  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
      --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(u(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(u(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(take(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(u(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(u(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(afterNth(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(u(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(u(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(sel(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(u(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(u(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(head(X)) , Marked_active(X)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(u(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(u(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(u(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(u(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(u(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(u(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(u(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(u(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(u(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(u(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(u(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(u(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(u(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(u(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(u(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(u(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(u(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(u(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(u(X1,X2,X3,X4)) , Marked_active(X1)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(u(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(u(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(splitAt(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(u(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(snd(X)) , Marked_active(X)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(u(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(u(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(pair(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(u(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(fst(X)) , Marked_active(X)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(u(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(u(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X2)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(take(X1,X2)) , Marked_active(X1)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X2)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(afterNth(X1,X2)) , Marked_active(X1)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X2)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(sel(X1,X2)) , Marked_active(X1)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(head(X)) , Marked_active(X)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(u(X1,X2,X3,X4)) , Marked_active(X1)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X2)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(splitAt(X1,X2)) , Marked_active(X1)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(snd(X)) , Marked_active(X)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X2)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(pair(X1,X2)) , Marked_active(X1)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(fst(X)) , Marked_active(X)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(natsFrom(X)) , Marked_active(X)> 
     --> <Marked_active(natsFrom(X)) , Marked_active(X)>
}

{  <Marked_natsFrom(ok(X)) , Marked_natsFrom(X)> 
      --> <Marked_natsFrom(ok(X)) , Marked_natsFrom(X)>
  <Marked_natsFrom(ok(X)) , Marked_natsFrom(X)> 
     --> <Marked_natsFrom(mark(X)) , Marked_natsFrom(X)>
  <Marked_natsFrom(mark(X)) , Marked_natsFrom(X)> 
     --> <Marked_natsFrom(ok(X)) , Marked_natsFrom(X)>
  <Marked_natsFrom(mark(X)) , Marked_natsFrom(X)> 
     --> <Marked_natsFrom(mark(X)) , Marked_natsFrom(X)>
}

{  <Marked_cons(ok(X1),ok(X2)) , Marked_cons(X1,X2)> 
      --> <Marked_cons(ok(X1),ok(X2)) , Marked_cons(X1,X2)>
  <Marked_cons(ok(X1),ok(X2)) , Marked_cons(X1,X2)> 
     --> <Marked_cons(mark(X1),X2) , Marked_cons(X1,X2)>
  <Marked_cons(mark(X1),X2) , Marked_cons(X1,X2)> 
     --> <Marked_cons(ok(X1),ok(X2)) , Marked_cons(X1,X2)>
  <Marked_cons(mark(X1),X2) , Marked_cons(X1,X2)> 
     --> <Marked_cons(mark(X1),X2) , Marked_cons(X1,X2)>
}

{  <Marked_s(ok(X)) , Marked_s(X)> --> <Marked_s(ok(X)) , Marked_s(X)>
  <Marked_s(ok(X)) , Marked_s(X)> --> <Marked_s(mark(X)) , Marked_s(X)>
  <Marked_s(mark(X)) , Marked_s(X)> --> <Marked_s(ok(X)) , Marked_s(X)>
  <Marked_s(mark(X)) , Marked_s(X)> --> <Marked_s(mark(X)) , Marked_s(X)>
}

{  <Marked_fst(ok(X)) , Marked_fst(X)> --> <Marked_fst(ok(X)) , Marked_fst(X)>
  <Marked_fst(ok(X)) , Marked_fst(X)> --> <Marked_fst(mark(X)) , Marked_fst(X)>
  <Marked_fst(mark(X)) , Marked_fst(X)> --> <Marked_fst(ok(X)) , Marked_fst(X)>
  <Marked_fst(mark(X)) , Marked_fst(X)> 
     --> <Marked_fst(mark(X)) , Marked_fst(X)>
}

{  <Marked_pair(ok(X1),ok(X2)) , Marked_pair(X1,X2)> 
      --> <Marked_pair(ok(X1),ok(X2)) , Marked_pair(X1,X2)>
  <Marked_pair(ok(X1),ok(X2)) , Marked_pair(X1,X2)> 
     --> <Marked_pair(X1,mark(X2)) , Marked_pair(X1,X2)>
  <Marked_pair(ok(X1),ok(X2)) , Marked_pair(X1,X2)> 
     --> <Marked_pair(mark(X1),X2) , Marked_pair(X1,X2)>
  <Marked_pair(X1,mark(X2)) , Marked_pair(X1,X2)> 
     --> <Marked_pair(ok(X1),ok(X2)) , Marked_pair(X1,X2)>
  <Marked_pair(X1,mark(X2)) , Marked_pair(X1,X2)> 
     --> <Marked_pair(X1,mark(X2)) , Marked_pair(X1,X2)>
  <Marked_pair(X1,mark(X2)) , Marked_pair(X1,X2)> 
     --> <Marked_pair(mark(X1),X2) , Marked_pair(X1,X2)>
  <Marked_pair(mark(X1),X2) , Marked_pair(X1,X2)> 
     --> <Marked_pair(ok(X1),ok(X2)) , Marked_pair(X1,X2)>
  <Marked_pair(mark(X1),X2) , Marked_pair(X1,X2)> 
     --> <Marked_pair(X1,mark(X2)) , Marked_pair(X1,X2)>
  <Marked_pair(mark(X1),X2) , Marked_pair(X1,X2)> 
     --> <Marked_pair(mark(X1),X2) , Marked_pair(X1,X2)>
}

{  <Marked_snd(ok(X)) , Marked_snd(X)> --> <Marked_snd(ok(X)) , Marked_snd(X)>
  <Marked_snd(ok(X)) , Marked_snd(X)> --> <Marked_snd(mark(X)) , Marked_snd(X)>
  <Marked_snd(mark(X)) , Marked_snd(X)> --> <Marked_snd(ok(X)) , Marked_snd(X)>
  <Marked_snd(mark(X)) , Marked_snd(X)> 
     --> <Marked_snd(mark(X)) , Marked_snd(X)>
}

{  <Marked_splitAt(ok(X1),ok(X2)) , Marked_splitAt(X1,X2)> 
      --> <Marked_splitAt(ok(X1),ok(X2)) , Marked_splitAt(X1,X2)>
  <Marked_splitAt(ok(X1),ok(X2)) , Marked_splitAt(X1,X2)> 
     --> <Marked_splitAt(X1,mark(X2)) , Marked_splitAt(X1,X2)>
  <Marked_splitAt(ok(X1),ok(X2)) , Marked_splitAt(X1,X2)> 
     --> <Marked_splitAt(mark(X1),X2) , Marked_splitAt(X1,X2)>
  <Marked_splitAt(X1,mark(X2)) , Marked_splitAt(X1,X2)> 
     --> <Marked_splitAt(ok(X1),ok(X2)) , Marked_splitAt(X1,X2)>
  <Marked_splitAt(X1,mark(X2)) , Marked_splitAt(X1,X2)> 
     --> <Marked_splitAt(X1,mark(X2)) , Marked_splitAt(X1,X2)>
  <Marked_splitAt(X1,mark(X2)) , Marked_splitAt(X1,X2)> 
     --> <Marked_splitAt(mark(X1),X2) , Marked_splitAt(X1,X2)>
  <Marked_splitAt(mark(X1),X2) , Marked_splitAt(X1,X2)> 
     --> <Marked_splitAt(ok(X1),ok(X2)) , Marked_splitAt(X1,X2)>
  <Marked_splitAt(mark(X1),X2) , Marked_splitAt(X1,X2)> 
     --> <Marked_splitAt(X1,mark(X2)) , Marked_splitAt(X1,X2)>
  <Marked_splitAt(mark(X1),X2) , Marked_splitAt(X1,X2)> 
     --> <Marked_splitAt(mark(X1),X2) , Marked_splitAt(X1,X2)>
}

{  <Marked_u(ok(X1),ok(X2),ok(X3),ok(X4)) , Marked_u(X1,X2,X3,X4)> 
      --> <Marked_u(ok(X1),ok(X2),ok(X3),ok(X4)) , Marked_u(X1,X2,X3,X4)>
  <Marked_u(ok(X1),ok(X2),ok(X3),ok(X4)) , Marked_u(X1,X2,X3,X4)> 
     --> <Marked_u(mark(X1),X2,X3,X4) , Marked_u(X1,X2,X3,X4)>
  <Marked_u(mark(X1),X2,X3,X4) , Marked_u(X1,X2,X3,X4)> 
     --> <Marked_u(ok(X1),ok(X2),ok(X3),ok(X4)) , Marked_u(X1,X2,X3,X4)>
  <Marked_u(mark(X1),X2,X3,X4) , Marked_u(X1,X2,X3,X4)> 
     --> <Marked_u(mark(X1),X2,X3,X4) , Marked_u(X1,X2,X3,X4)>
}

{  <Marked_head(ok(X)) , Marked_head(X)> 
      --> <Marked_head(ok(X)) , Marked_head(X)>
  <Marked_head(ok(X)) , Marked_head(X)> 
     --> <Marked_head(mark(X)) , Marked_head(X)>
  <Marked_head(mark(X)) , Marked_head(X)> 
     --> <Marked_head(ok(X)) , Marked_head(X)>
  <Marked_head(mark(X)) , Marked_head(X)> 
     --> <Marked_head(mark(X)) , Marked_head(X)>
}

{  <Marked_tail(ok(X)) , Marked_tail(X)> 
      --> <Marked_tail(ok(X)) , Marked_tail(X)>
  <Marked_tail(ok(X)) , Marked_tail(X)> 
     --> <Marked_tail(mark(X)) , Marked_tail(X)>
  <Marked_tail(mark(X)) , Marked_tail(X)> 
     --> <Marked_tail(ok(X)) , Marked_tail(X)>
  <Marked_tail(mark(X)) , Marked_tail(X)> 
     --> <Marked_tail(mark(X)) , Marked_tail(X)>
}

{  <Marked_sel(ok(X1),ok(X2)) , Marked_sel(X1,X2)> 
      --> <Marked_sel(ok(X1),ok(X2)) , Marked_sel(X1,X2)>
  <Marked_sel(ok(X1),ok(X2)) , Marked_sel(X1,X2)> 
     --> <Marked_sel(X1,mark(X2)) , Marked_sel(X1,X2)>
  <Marked_sel(ok(X1),ok(X2)) , Marked_sel(X1,X2)> 
     --> <Marked_sel(mark(X1),X2) , Marked_sel(X1,X2)>
  <Marked_sel(X1,mark(X2)) , Marked_sel(X1,X2)> 
     --> <Marked_sel(ok(X1),ok(X2)) , Marked_sel(X1,X2)>
  <Marked_sel(X1,mark(X2)) , Marked_sel(X1,X2)> 
     --> <Marked_sel(X1,mark(X2)) , Marked_sel(X1,X2)>
  <Marked_sel(X1,mark(X2)) , Marked_sel(X1,X2)> 
     --> <Marked_sel(mark(X1),X2) , Marked_sel(X1,X2)>
  <Marked_sel(mark(X1),X2) , Marked_sel(X1,X2)> 
     --> <Marked_sel(ok(X1),ok(X2)) , Marked_sel(X1,X2)>
  <Marked_sel(mark(X1),X2) , Marked_sel(X1,X2)> 
     --> <Marked_sel(X1,mark(X2)) , Marked_sel(X1,X2)>
  <Marked_sel(mark(X1),X2) , Marked_sel(X1,X2)> 
     --> <Marked_sel(mark(X1),X2) , Marked_sel(X1,X2)>
}

{  <Marked_afterNth(ok(X1),ok(X2)) , Marked_afterNth(X1,X2)> 
      --> <Marked_afterNth(ok(X1),ok(X2)) , Marked_afterNth(X1,X2)>
  <Marked_afterNth(ok(X1),ok(X2)) , Marked_afterNth(X1,X2)> 
     --> <Marked_afterNth(X1,mark(X2)) , Marked_afterNth(X1,X2)>
  <Marked_afterNth(ok(X1),ok(X2)) , Marked_afterNth(X1,X2)> 
     --> <Marked_afterNth(mark(X1),X2) , Marked_afterNth(X1,X2)>
  <Marked_afterNth(X1,mark(X2)) , Marked_afterNth(X1,X2)> 
     --> <Marked_afterNth(ok(X1),ok(X2)) , Marked_afterNth(X1,X2)>
  <Marked_afterNth(X1,mark(X2)) , Marked_afterNth(X1,X2)> 
     --> <Marked_afterNth(X1,mark(X2)) , Marked_afterNth(X1,X2)>
  <Marked_afterNth(X1,mark(X2)) , Marked_afterNth(X1,X2)> 
     --> <Marked_afterNth(mark(X1),X2) , Marked_afterNth(X1,X2)>
  <Marked_afterNth(mark(X1),X2) , Marked_afterNth(X1,X2)> 
     --> <Marked_afterNth(ok(X1),ok(X2)) , Marked_afterNth(X1,X2)>
  <Marked_afterNth(mark(X1),X2) , Marked_afterNth(X1,X2)> 
     --> <Marked_afterNth(X1,mark(X2)) , Marked_afterNth(X1,X2)>
  <Marked_afterNth(mark(X1),X2) , Marked_afterNth(X1,X2)> 
     --> <Marked_afterNth(mark(X1),X2) , Marked_afterNth(X1,X2)>
}

{  <Marked_take(ok(X1),ok(X2)) , Marked_take(X1,X2)> 
      --> <Marked_take(ok(X1),ok(X2)) , Marked_take(X1,X2)>
  <Marked_take(ok(X1),ok(X2)) , Marked_take(X1,X2)> 
     --> <Marked_take(X1,mark(X2)) , Marked_take(X1,X2)>
  <Marked_take(ok(X1),ok(X2)) , Marked_take(X1,X2)> 
     --> <Marked_take(mark(X1),X2) , Marked_take(X1,X2)>
  <Marked_take(X1,mark(X2)) , Marked_take(X1,X2)> 
     --> <Marked_take(ok(X1),ok(X2)) , Marked_take(X1,X2)>
  <Marked_take(X1,mark(X2)) , Marked_take(X1,X2)> 
     --> <Marked_take(X1,mark(X2)) , Marked_take(X1,X2)>
  <Marked_take(X1,mark(X2)) , Marked_take(X1,X2)> 
     --> <Marked_take(mark(X1),X2) , Marked_take(X1,X2)>
  <Marked_take(mark(X1),X2) , Marked_take(X1,X2)> 
     --> <Marked_take(ok(X1),ok(X2)) , Marked_take(X1,X2)>
  <Marked_take(mark(X1),X2) , Marked_take(X1,X2)> 
     --> <Marked_take(X1,mark(X2)) , Marked_take(X1,X2)>
  <Marked_take(mark(X1),X2) , Marked_take(X1,X2)> 
     --> <Marked_take(mark(X1),X2) , Marked_take(X1,X2)>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  cons(mark(X1),X2) >= mark(cons(X1,X2)) ;
  cons(ok(X1),ok(X2)) >= ok(cons(X1,X2)) ;
  natsFrom(mark(X)) >= mark(natsFrom(X)) ;
  natsFrom(ok(X)) >= ok(natsFrom(X)) ;
  s(mark(X)) >= mark(s(X)) ;
  s(ok(X)) >= ok(s(X)) ;
  active(cons(X1,X2)) >= cons(active(X1),X2) ;
  active(natsFrom(N)) >= mark(cons(N,natsFrom(s(N)))) ;
  active(natsFrom(X)) >= natsFrom(active(X)) ;
  active(s(X)) >= s(active(X)) ;
  active(fst(pair(XS,YS))) >= mark(XS) ;
  active(fst(X)) >= fst(active(X)) ;
  active(pair(X1,X2)) >= pair(active(X1),X2) ;
  active(pair(X1,X2)) >= pair(X1,active(X2)) ;
  active(snd(pair(XS,YS))) >= mark(YS) ;
  active(snd(X)) >= snd(active(X)) ;
  active(splitAt(s(N),cons(X,XS))) >= mark(u(splitAt(N,XS),N,X,XS)) ;
  active(splitAt(0,XS)) >= mark(pair(nil,XS)) ;
  active(splitAt(X1,X2)) >= splitAt(active(X1),X2) ;
  active(splitAt(X1,X2)) >= splitAt(X1,active(X2)) ;
  active(u(pair(YS,ZS),N,X,XS)) >= mark(pair(cons(X,YS),ZS)) ;
  active(u(X1,X2,X3,X4)) >= u(active(X1),X2,X3,X4) ;
  active(head(cons(N,XS))) >= mark(N) ;
  active(head(X)) >= head(active(X)) ;
  active(tail(cons(N,XS))) >= mark(XS) ;
  active(tail(X)) >= tail(active(X)) ;
  active(afterNth(N,XS)) >= mark(snd(splitAt(N,XS))) ;
  active(afterNth(X1,X2)) >= afterNth(active(X1),X2) ;
  active(afterNth(X1,X2)) >= afterNth(X1,active(X2)) ;
  active(sel(N,XS)) >= mark(head(afterNth(N,XS))) ;
  active(sel(X1,X2)) >= sel(active(X1),X2) ;
  active(sel(X1,X2)) >= sel(X1,active(X2)) ;
  active(take(N,XS)) >= mark(fst(splitAt(N,XS))) ;
  active(take(X1,X2)) >= take(active(X1),X2) ;
  active(take(X1,X2)) >= take(X1,active(X2)) ;
  fst(mark(X)) >= mark(fst(X)) ;
  fst(ok(X)) >= ok(fst(X)) ;
  pair(mark(X1),X2) >= mark(pair(X1,X2)) ;
  pair(ok(X1),ok(X2)) >= ok(pair(X1,X2)) ;
  pair(X1,mark(X2)) >= mark(pair(X1,X2)) ;
  snd(mark(X)) >= mark(snd(X)) ;
  snd(ok(X)) >= ok(snd(X)) ;
  splitAt(mark(X1),X2) >= mark(splitAt(X1,X2)) ;
  splitAt(ok(X1),ok(X2)) >= ok(splitAt(X1,X2)) ;
  splitAt(X1,mark(X2)) >= mark(splitAt(X1,X2)) ;
  u(mark(X1),X2,X3,X4) >= mark(u(X1,X2,X3,X4)) ;
  u(ok(X1),ok(X2),ok(X3),ok(X4)) >= ok(u(X1,X2,X3,X4)) ;
  head(mark(X)) >= mark(head(X)) ;
  head(ok(X)) >= ok(head(X)) ;
  tail(mark(X)) >= mark(tail(X)) ;
  tail(ok(X)) >= ok(tail(X)) ;
  afterNth(mark(X1),X2) >= mark(afterNth(X1,X2)) ;
  afterNth(ok(X1),ok(X2)) >= ok(afterNth(X1,X2)) ;
  afterNth(X1,mark(X2)) >= mark(afterNth(X1,X2)) ;
  sel(mark(X1),X2) >= mark(sel(X1,X2)) ;
  sel(ok(X1),ok(X2)) >= ok(sel(X1,X2)) ;
  sel(X1,mark(X2)) >= mark(sel(X1,X2)) ;
  take(mark(X1),X2) >= mark(take(X1,X2)) ;
  take(ok(X1),ok(X2)) >= ok(take(X1,X2)) ;
  take(X1,mark(X2)) >= mark(take(X1,X2)) ;
  proper(cons(X1,X2)) >= cons(proper(X1),proper(X2)) ;
  proper(natsFrom(X)) >= natsFrom(proper(X)) ;
  proper(s(X)) >= s(proper(X)) ;
  proper(fst(X)) >= fst(proper(X)) ;
  proper(pair(X1,X2)) >= pair(proper(X1),proper(X2)) ;
  proper(snd(X)) >= snd(proper(X)) ;
  proper(nil) >= ok(nil) ;
  proper(splitAt(X1,X2)) >= splitAt(proper(X1),proper(X2)) ;
  proper(0) >= ok(0) ;
  proper(u(X1,X2,X3,X4)) >= u(proper(X1),proper(X2),proper(X3),proper(X4)) ;
  proper(head(X)) >= head(proper(X)) ;
  proper(tail(X)) >= tail(proper(X)) ;
  proper(afterNth(X1,X2)) >= afterNth(proper(X1),proper(X2)) ;
  proper(sel(X1,X2)) >= sel(proper(X1),proper(X2)) ;
  proper(take(X1,X2)) >= take(proper(X1),proper(X2)) ;
  top(mark(X)) >= top(proper(X)) ;
  top(ok(X)) >= top(active(X)) ;
  Marked_top(mark(X)) >= Marked_top(proper(X)) ;
  Marked_top(ok(X)) >= Marked_top(active(X)) ;
 }
 + Disjunctions:{ 
{
  Marked_top(mark(X)) > Marked_top(proper(X)) ;
 }
{
  Marked_top(ok(X)) > Marked_top(active(X)) ;
 }
 } 
=== TIMER virtual : 10.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 10.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
Entering rpo_solver
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 15.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 15.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
=== TIMER virtual : 50.000000 ===
trying sub matrices of size: 1
Matrix interpretation constraints generated.
Search parameters: LINEAR MATRIX 3x3 (strict=1x1) ; time limit: 50.. 
Termination constraints generated.
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 50.000000 ===
=== STOPING TIMER real ===
Sat timeout reached
=== STOPING TIMER virtual ===
No solution found for these parameters.
No solution found for these constraints.
APPLY CRITERIA (Simple graph)
Found the following constraints:
{
  cons(mark(X1),X2) >= mark(cons(X1,X2)) ;
  cons(ok(X1),ok(X2)) >= ok(cons(X1,X2)) ;
  natsFrom(mark(X)) >= mark(natsFrom(X)) ;
  natsFrom(ok(X)) >= ok(natsFrom(X)) ;
  s(mark(X)) >= mark(s(X)) ;
  s(ok(X)) >= ok(s(X)) ;
  active(cons(X1,X2)) >= cons(active(X1),X2) ;
  active(natsFrom(N)) >= mark(cons(N,natsFrom(s(N)))) ;
  active(natsFrom(X)) >= natsFrom(active(X)) ;
  active(s(X)) >= s(active(X)) ;
  active(fst(pair(XS,YS))) >= mark(XS) ;
  active(fst(X)) >= fst(active(X)) ;
  active(pair(X1,X2)) >= pair(active(X1),X2) ;
  active(pair(X1,X2)) >= pair(X1,active(X2)) ;
  active(snd(pair(XS,YS))) >= mark(YS) ;
  active(snd(X)) >= snd(active(X)) ;
  active(splitAt(s(N),cons(X,XS))) >= mark(u(splitAt(N,XS),N,X,XS)) ;
  active(splitAt(0,XS)) >= mark(pair(nil,XS)) ;
  active(splitAt(X1,X2)) >= splitAt(active(X1),X2) ;
  active(splitAt(X1,X2)) >= splitAt(X1,active(X2)) ;
  active(u(pair(YS,ZS),N,X,XS)) >= mark(pair(cons(X,YS),ZS)) ;
  active(u(X1,X2,X3,X4)) >= u(active(X1),X2,X3,X4) ;
  active(head(cons(N,XS))) >= mark(N) ;
  active(head(X)) >= head(active(X)) ;
  active(tail(cons(N,XS))) >= mark(XS) ;
  active(tail(X)) >= tail(active(X)) ;
  active(afterNth(N,XS)) >= mark(snd(splitAt(N,XS))) ;
  active(afterNth(X1,X2)) >= afterNth(active(X1),X2) ;
  active(afterNth(X1,X2)) >= afterNth(X1,active(X2)) ;
  active(sel(N,XS)) >= mark(head(afterNth(N,XS))) ;
  active(sel(X1,X2)) >= sel(active(X1),X2) ;
  active(sel(X1,X2)) >= sel(X1,active(X2)) ;
  active(take(N,XS)) >= mark(fst(splitAt(N,XS))) ;
  active(take(X1,X2)) >= take(active(X1),X2) ;
  active(take(X1,X2)) >= take(X1,active(X2)) ;
  fst(mark(X)) >= mark(fst(X)) ;
  fst(ok(X)) >= ok(fst(X)) ;
  pair(mark(X1),X2) >= mark(pair(X1,X2)) ;
  pair(ok(X1),ok(X2)) >= ok(pair(X1,X2)) ;
  pair(X1,mark(X2)) >= mark(pair(X1,X2)) ;
  snd(mark(X)) >= mark(snd(X)) ;
  snd(ok(X)) >= ok(snd(X)) ;
  splitAt(mark(X1),X2) >= mark(splitAt(X1,X2)) ;
  splitAt(ok(X1),ok(X2)) >= ok(splitAt(X1,X2)) ;
  splitAt(X1,mark(X2)) >= mark(splitAt(X1,X2)) ;
  u(mark(X1),X2,X3,X4) >= mark(u(X1,X2,X3,X4)) ;
  u(ok(X1),ok(X2),ok(X3),ok(X4)) >= ok(u(X1,X2,X3,X4)) ;
  head(mark(X)) >= mark(head(X)) ;
  head(ok(X)) >= ok(head(X)) ;
  tail(mark(X)) >= mark(tail(X)) ;
  tail(ok(X)) >= ok(tail(X)) ;
  afterNth(mark(X1),X2) >= mark(afterNth(X1,X2)) ;
  afterNth(ok(X1),ok(X2)) >= ok(afterNth(X1,X2)) ;
  afterNth(X1,mark(X2)) >= mark(afterNth(X1,X2)) ;
  sel(mark(X1),X2) >= mark(sel(X1,X2)) ;
  sel(ok(X1),ok(X2)) >= ok(sel(X1,X2)) ;
  sel(X1,mark(X2)) >= mark(sel(X1,X2)) ;
  take(mark(X1),X2) >= mark(take(X1,X2)) ;
  take(ok(X1),ok(X2)) >= ok(take(X1,X2)) ;
  take(X1,mark(X2)) >= mark(take(X1,X2)) ;
  proper(cons(X1,X2)) >= cons(proper(X1),proper(X2)) ;
  proper(natsFrom(X)) >= natsFrom(proper(X)) ;
  proper(s(X)) >= s(proper(X)) ;
  proper(fst(X)) >= fst(proper(X)) ;
  proper(pair(X1,X2)) >= pair(proper(X1),proper(X2)) ;
  proper(snd(X)) >= snd(proper(X)) ;
  proper(nil) >= ok(nil) ;
  proper(splitAt(X1,X2)) >= splitAt(proper(X1),proper(X2)) ;
  proper(0) >= ok(0) ;
  proper(u(X1,X2,X3,X4)) >= u(proper(X1),proper(X2),proper(X3),proper(X4)) ;
  proper(head(X)) >= head(proper(X)) ;
  proper(tail(X)) >= tail(proper(X)) ;
  proper(afterNth(X1,X2)) >= afterNth(proper(X1),proper(X2)) ;
  proper(sel(X1,X2)) >= sel(proper(X1),proper(X2)) ;
  proper(take(X1,X2)) >= take(proper(X1),proper(X2)) ;
  top(mark(X)) >= top(proper(X)) ;
  top(ok(X)) >= top(active(X)) ;
  Marked_top(mark(X)) > Marked_top(proper(X)) ;
  Marked_top(ok(X)) > Marked_top(active(X)) ;
 }

APPLY CRITERIA (SOLVE_ORD)
Trying to solve the following constraints:
{
  cons(mark(X1),X2) >= mark(cons(X1,X2)) ;
  cons(ok(X1),ok(X2)) >= ok(cons(X1,X2)) ;
  natsFrom(mark(X)) >= mark(natsFrom(X)) ;
  natsFrom(ok(X)) >= ok(natsFrom(X)) ;
  s(mark(X)) >= mark(s(X)) ;
  s(ok(X)) >= ok(s(X)) ;
  active(cons(X1,X2)) >= cons(active(X1),X2) ;
  active(natsFrom(N)) >= mark(cons(N,natsFrom(s(N)))) ;
  active(natsFrom(X)) >= natsFrom(active(X)) ;
  active(s(X)) >= s(active(X)) ;
  active(fst(pair(XS,YS))) >= mark(XS) ;
  active(fst(X)) >= fst(active(X)) ;
  active(pair(X1,X2)) >= pair(active(X1),X2) ;
  active(pair(X1,X2)) >= pair(X1,active(X2)) ;
  active(snd(pair(XS,YS))) >= mark(YS) ;
  active(snd(X)) >= snd(active(X)) ;
  active(splitAt(s(N),cons(X,XS))) >= mark(u(splitAt(N,XS),N,X,XS)) ;
  active(splitAt(0,XS)) >= mark(pair(nil,XS)) ;
  active(splitAt(X1,X2)) >= splitAt(active(X1),X2) ;
  active(splitAt(X1,X2)) >= splitAt(X1,active(X2)) ;
  active(u(pair(YS,ZS),N,X,XS)) >= mark(pair(cons(X,YS),ZS)) ;
  active(u(X1,X2,X3,X4)) >= u(active(X1),X2,X3,X4) ;
  active(head(cons(N,XS))) >= mark(N) ;
  active(head(X)) >= head(active(X)) ;
  active(tail(cons(N,XS))) >= mark(XS) ;
  active(tail(X)) >= tail(active(X)) ;
  active(afterNth(N,XS)) >= mark(snd(splitAt(N,XS))) ;
  active(afterNth(X1,X2)) >= afterNth(active(X1),X2) ;
  active(afterNth(X1,X2)) >= afterNth(X1,active(X2)) ;
  active(sel(N,XS)) >= mark(head(afterNth(N,XS))) ;
  active(sel(X1,X2)) >= sel(active(X1),X2) ;
  active(sel(X1,X2)) >= sel(X1,active(X2)) ;
  active(take(N,XS)) >= mark(fst(splitAt(N,XS))) ;
  active(take(X1,X2)) >= take(active(X1),X2) ;
  active(take(X1,X2)) >= take(X1,active(X2)) ;
  fst(mark(X)) >= mark(fst(X)) ;
  fst(ok(X)) >= ok(fst(X)) ;
  pair(mark(X1),X2) >= mark(pair(X1,X2)) ;
  pair(ok(X1),ok(X2)) >= ok(pair(X1,X2)) ;
  pair(X1,mark(X2)) >= mark(pair(X1,X2)) ;
  snd(mark(X)) >= mark(snd(X)) ;
  snd(ok(X)) >= ok(snd(X)) ;
  splitAt(mark(X1),X2) >= mark(splitAt(X1,X2)) ;
  splitAt(ok(X1),ok(X2)) >= ok(splitAt(X1,X2)) ;
  splitAt(X1,mark(X2)) >= mark(splitAt(X1,X2)) ;
  u(mark(X1),X2,X3,X4) >= mark(u(X1,X2,X3,X4)) ;
  u(ok(X1),ok(X2),ok(X3),ok(X4)) >= ok(u(X1,X2,X3,X4)) ;
  head(mark(X)) >= mark(head(X)) ;
  head(ok(X)) >= ok(head(X)) ;
  tail(mark(X)) >= mark(tail(X)) ;
  tail(ok(X)) >= ok(tail(X)) ;
  afterNth(mark(X1),X2) >= mark(afterNth(X1,X2)) ;
  afterNth(ok(X1),ok(X2)) >= ok(afterNth(X1,X2)) ;
  afterNth(X1,mark(X2)) >= mark(afterNth(X1,X2)) ;
  sel(mark(X1),X2) >= mark(sel(X1,X2)) ;
  sel(ok(X1),ok(X2)) >= ok(sel(X1,X2)) ;
  sel(X1,mark(X2)) >= mark(sel(X1,X2)) ;
  take(mark(X1),X2) >= mark(take(X1,X2)) ;
  take(ok(X1),ok(X2)) >= ok(take(X1,X2)) ;
  take(X1,mark(X2)) >= mark(take(X1,X2)) ;
  proper(cons(X1,X2)) >= cons(proper(X1),proper(X2)) ;
  proper(natsFrom(X)) >= natsFrom(proper(X)) ;
  proper(s(X)) >= s(proper(X)) ;
  proper(fst(X)) >= fst(proper(X)) ;
  proper(pair(X1,X2)) >= pair(proper(X1),proper(X2)) ;
  proper(snd(X)) >= snd(proper(X)) ;
  proper(nil) >= ok(nil) ;
  proper(splitAt(X1,X2)) >= splitAt(proper(X1),proper(X2)) ;
  proper(0) >= ok(0) ;
  proper(u(X1,X2,X3,X4)) >= u(proper(X1),proper(X2),proper(X3),proper(X4)) ;
  proper(head(X)) >= head(proper(X)) ;
  proper(tail(X)) >= tail(proper(X)) ;
  proper(afterNth(X1,X2)) >= afterNth(proper(X1),proper(X2)) ;
  proper(sel(X1,X2)) >= sel(proper(X1),proper(X2)) ;
  proper(take(X1,X2)) >= take(proper(X1),proper(X2)) ;
  top(mark(X)) >= top(proper(X)) ;
  top(ok(X)) >= top(active(X)) ;
  Marked_top(mark(X)) > Marked_top(proper(X)) ;
  Marked_top(ok(X)) > Marked_top(active(X)) ;
 }
 + Disjunctions:{ 
 } 
=== 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 ===
No solution found for these parameters.(10647 bt (15312) [63])
=== TIMER virtual : 15.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 15.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
=== TIMER virtual : 50.000000 ===
trying sub matrices of size: 1
Matrix interpretation constraints generated.
Search parameters: LINEAR MATRIX 3x3 (strict=1x1) ; time limit: 50.. 
Termination constraints generated.
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 50.000000 ===
=== STOPING TIMER real ===
Sat timeout reached
=== 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 122.974322 seconds (real time)
Cime Exit Status: 0