Problem: nats() -> cons(0(),n__incr(nats())) pairs() -> cons(0(),n__incr(odds())) odds() -> incr(pairs()) incr(cons(X,XS)) -> cons(s(X),n__incr(activate(XS))) head(cons(X,XS)) -> X tail(cons(X,XS)) -> activate(XS) incr(X) -> n__incr(X) activate(n__incr(X)) -> incr(X) activate(X) -> X Proof: Containment Processor: loop length: 1 terms: nats() context: cons(0(),n__incr([])) substitution: Qed