Input TRS:
    1: nats() -> adx(zeros())
    2: zeros() -> cons(n__0(),n__zeros())
    3: incr(cons(X,Y)) -> cons(n__s(activate(X)),n__incr(activate(Y)))
    4: adx(cons(X,Y)) -> incr(cons(activate(X),n__adx(activate(Y))))
    5: hd(cons(X,Y)) -> activate(X)
    6: tl(cons(X,Y)) -> activate(Y)
    7: 0() -> n__0()
    8: zeros() -> n__zeros()
    9: s(X) -> n__s(X)
    10: incr(X) -> n__incr(X)
    11: adx(X) -> n__adx(X)
    12: activate(n__0()) -> 0()
    13: activate(n__zeros()) -> zeros()
    14: activate(n__s(X)) -> s(X)
    15: activate(n__incr(X)) -> incr(X)
    16: activate(n__adx(X)) -> adx(X)
    17: activate(X) -> X
Number of Rules: 17
Direct POLO(Pol) ... failed.