(VAR X L X1 X2)
(RULES 
active(incr(nil)) -> mark(nil)
active(incr(cons(X,L))) -> mark(cons(s(X),incr(L)))
active(adx(nil)) -> mark(nil)
active(adx(cons(X,L))) -> mark(incr(cons(X,adx(L))))
active(nats) -> mark(adx(zeros))
active(zeros) -> mark(cons(0,zeros))
active(head(cons(X,L))) -> mark(X)
active(tail(cons(X,L))) -> mark(L)
active(incr(X)) -> incr(active(X))
active(cons(X1,X2)) -> cons(active(X1),X2)
active(s(X)) -> s(active(X))
active(adx(X)) -> adx(active(X))
active(head(X)) -> head(active(X))
active(tail(X)) -> tail(active(X))
incr(mark(X)) -> mark(incr(X))
cons(mark(X1),X2) -> mark(cons(X1,X2))
s(mark(X)) -> mark(s(X))
adx(mark(X)) -> mark(adx(X))
head(mark(X)) -> mark(head(X))
tail(mark(X)) -> mark(tail(X))
proper(incr(X)) -> incr(proper(X))
proper(nil) -> ok(nil)
proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
proper(s(X)) -> s(proper(X))
proper(adx(X)) -> adx(proper(X))
proper(nats) -> ok(nats)
proper(zeros) -> ok(zeros)
proper(0) -> ok(0)
proper(head(X)) -> head(proper(X))
proper(tail(X)) -> tail(proper(X))
incr(ok(X)) -> ok(incr(X))
cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
s(ok(X)) -> ok(s(X))
adx(ok(X)) -> ok(adx(X))
head(ok(X)) -> ok(head(X))
tail(ok(X)) -> ok(tail(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
)