(VAR N X XS YS ZS Y X1 X2 X3 X4)
(RULES 
active(U11(tt,N,X,XS)) -> mark(U12(splitAt(N,XS),X))
active(U12(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
active(afterNth(N,XS)) -> mark(snd(splitAt(N,XS)))
active(and(tt,X)) -> mark(X)
active(fst(pair(X,Y))) -> mark(X)
active(head(cons(N,XS))) -> mark(N)
active(natsFrom(N)) -> mark(cons(N,natsFrom(s(N))))
active(sel(N,XS)) -> mark(head(afterNth(N,XS)))
active(snd(pair(X,Y))) -> mark(Y)
active(splitAt(0,XS)) -> mark(pair(nil,XS))
active(splitAt(s(N),cons(X,XS))) -> mark(U11(tt,N,X,XS))
active(tail(cons(N,XS))) -> mark(XS)
active(take(N,XS)) -> mark(fst(splitAt(N,XS)))
active(U11(X1,X2,X3,X4)) -> U11(active(X1),X2,X3,X4)
active(U12(X1,X2)) -> U12(active(X1),X2)
active(splitAt(X1,X2)) -> splitAt(active(X1),X2)
active(splitAt(X1,X2)) -> splitAt(X1,active(X2))
active(pair(X1,X2)) -> pair(active(X1),X2)
active(pair(X1,X2)) -> pair(X1,active(X2))
active(cons(X1,X2)) -> cons(active(X1),X2)
active(afterNth(X1,X2)) -> afterNth(active(X1),X2)
active(afterNth(X1,X2)) -> afterNth(X1,active(X2))
active(snd(X)) -> snd(active(X))
active(and(X1,X2)) -> and(active(X1),X2)
active(fst(X)) -> fst(active(X))
active(head(X)) -> head(active(X))
active(natsFrom(X)) -> natsFrom(active(X))
active(s(X)) -> s(active(X))
active(sel(X1,X2)) -> sel(active(X1),X2)
active(sel(X1,X2)) -> sel(X1,active(X2))
active(tail(X)) -> tail(active(X))
active(take(X1,X2)) -> take(active(X1),X2)
active(take(X1,X2)) -> take(X1,active(X2))
U11(mark(X1),X2,X3,X4) -> mark(U11(X1,X2,X3,X4))
U12(mark(X1),X2) -> mark(U12(X1,X2))
splitAt(mark(X1),X2) -> mark(splitAt(X1,X2))
splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2))
pair(mark(X1),X2) -> mark(pair(X1,X2))
pair(X1,mark(X2)) -> mark(pair(X1,X2))
cons(mark(X1),X2) -> mark(cons(X1,X2))
afterNth(mark(X1),X2) -> mark(afterNth(X1,X2))
afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2))
snd(mark(X)) -> mark(snd(X))
and(mark(X1),X2) -> mark(and(X1,X2))
fst(mark(X)) -> mark(fst(X))
head(mark(X)) -> mark(head(X))
natsFrom(mark(X)) -> mark(natsFrom(X))
s(mark(X)) -> mark(s(X))
sel(mark(X1),X2) -> mark(sel(X1,X2))
sel(X1,mark(X2)) -> mark(sel(X1,X2))
tail(mark(X)) -> mark(tail(X))
take(mark(X1),X2) -> mark(take(X1,X2))
take(X1,mark(X2)) -> mark(take(X1,X2))
proper(U11(X1,X2,X3,X4)) -> U11(proper(X1),proper(X2),proper(X3),proper(X4))
proper(tt) -> ok(tt)
proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2))
proper(pair(X1,X2)) -> pair(proper(X1),proper(X2))
proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2))
proper(snd(X)) -> snd(proper(X))
proper(and(X1,X2)) -> and(proper(X1),proper(X2))
proper(fst(X)) -> fst(proper(X))
proper(head(X)) -> head(proper(X))
proper(natsFrom(X)) -> natsFrom(proper(X))
proper(s(X)) -> s(proper(X))
proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
proper(0) -> ok(0)
proper(nil) -> ok(nil)
proper(tail(X)) -> tail(proper(X))
proper(take(X1,X2)) -> take(proper(X1),proper(X2))
U11(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U11(X1,X2,X3,X4))
U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2))
pair(ok(X1),ok(X2)) -> ok(pair(X1,X2))
cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2))
snd(ok(X)) -> ok(snd(X))
and(ok(X1),ok(X2)) -> ok(and(X1,X2))
fst(ok(X)) -> ok(fst(X))
head(ok(X)) -> ok(head(X))
natsFrom(ok(X)) -> ok(natsFrom(X))
s(ok(X)) -> ok(s(X))
sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
tail(ok(X)) -> ok(tail(X))
take(ok(X1),ok(X2)) -> ok(take(X1,X2))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
)
(STRATEGY INNERMOST)