(VAR X Y Z X1 X2)
(RULES 
active(dbl(0)) -> mark(0)
active(dbl(s(X))) -> mark(s(s(dbl(X))))
active(dbls(nil)) -> mark(nil)
active(dbls(cons(X,Y))) -> mark(cons(dbl(X),dbls(Y)))
active(sel(0,cons(X,Y))) -> mark(X)
active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z))
active(indx(nil,X)) -> mark(nil)
active(indx(cons(X,Y),Z)) -> mark(cons(sel(X,Z),indx(Y,Z)))
active(from(X)) -> mark(cons(X,from(s(X))))
active(dbl(X)) -> dbl(active(X))
active(dbls(X)) -> dbls(active(X))
active(sel(X1,X2)) -> sel(active(X1),X2)
active(sel(X1,X2)) -> sel(X1,active(X2))
active(indx(X1,X2)) -> indx(active(X1),X2)
dbl(mark(X)) -> mark(dbl(X))
dbls(mark(X)) -> mark(dbls(X))
sel(mark(X1),X2) -> mark(sel(X1,X2))
sel(X1,mark(X2)) -> mark(sel(X1,X2))
indx(mark(X1),X2) -> mark(indx(X1,X2))
proper(dbl(X)) -> dbl(proper(X))
proper(0) -> ok(0)
proper(s(X)) -> s(proper(X))
proper(dbls(X)) -> dbls(proper(X))
proper(nil) -> ok(nil)
proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
proper(indx(X1,X2)) -> indx(proper(X1),proper(X2))
proper(from(X)) -> from(proper(X))
dbl(ok(X)) -> ok(dbl(X))
s(ok(X)) -> ok(s(X))
dbls(ok(X)) -> ok(dbls(X))
cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
indx(ok(X1),ok(X2)) -> ok(indx(X1,X2))
from(ok(X)) -> ok(from(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
)