(STRATEGY
    INNERMOST)

(VAR
    X X1 X2 Y)
(DATATYPES
    A = µX.< cons(X, X), 0, zeros, s(X), incr(X), adx(X), nats, hd(X), tl(X) >)
(SIGNATURES
    a__nats :: [] -> A
    a__zeros :: [] -> A
    a__incr :: [A] -> A
    a__adx :: [A] -> A
    a__hd :: [A] -> A
    a__tl :: [A] -> A
    mark :: [A] -> A)
(RULES
    a__nats() -> a__adx(a__zeros())
    a__zeros() -> cons(0(),zeros())
    a__incr(cons(X,Y)) -> cons(s(X)
                              ,incr(Y))
    a__adx(cons(X,Y)) ->
      a__incr(cons(X,adx(Y)))
    a__hd(cons(X,Y)) -> mark(X)
    a__tl(cons(X,Y)) -> mark(Y)
    mark(nats()) -> a__nats()
    mark(adx(X)) -> a__adx(mark(X))
    mark(zeros()) -> a__zeros()
    mark(incr(X)) ->
      a__incr(mark(X))
    mark(hd(X)) -> a__hd(mark(X))
    mark(tl(X)) -> a__tl(mark(X))
    mark(cons(X1,X2)) -> cons(X1,X2)
    mark(0()) -> 0()
    mark(s(X)) -> s(X)
    a__nats() -> nats()
    a__adx(X) -> adx(X)
    a__zeros() -> zeros()
    a__incr(X) -> incr(X)
    a__hd(X) -> hd(X)
    a__tl(X) -> tl(X))