(STRATEGY
    INNERMOST)

(VAR
    X Y)
(DATATYPES
    A = µX.< cons(X, X), n__0, n__zeros, n__s(X), n__incr(X), n__adx(X) >)
(SIGNATURES
    nats :: [] -> A
    zeros :: [] -> A
    incr :: [A] -> A
    adx :: [A] -> A
    hd :: [A] -> A
    tl :: [A] -> A
    0 :: [] -> A
    s :: [A] -> A
    activate :: [A] -> A)
(RULES
    nats() -> adx(zeros())
    zeros() -> cons(n__0()
                   ,n__zeros())
    incr(cons(X,Y)) ->
      cons(n__s(activate(X))
          ,n__incr(activate(Y)))
    adx(cons(X,Y)) ->
      incr(cons(activate(X)
               ,n__adx(activate(Y))))
    hd(cons(X,Y)) -> activate(X)
    tl(cons(X,Y)) -> activate(Y)
    0() -> n__0()
    zeros() -> n__zeros()
    s(X) -> n__s(X)
    incr(X) -> n__incr(X)
    adx(X) -> n__adx(X)
    activate(n__0()) -> 0()
    activate(n__zeros()) -> zeros()
    activate(n__s(X)) -> s(X)
    activate(n__incr(X)) -> incr(X)
    activate(n__adx(X)) -> adx(X)
    activate(X) -> X)