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