(STRATEGY
    INNERMOST)

(VAR
    L X X1 X2)
(DATATYPES
    A = µX.< nil, cons(X, X), s(X), incr(X), adx(X), 0, zeros, nats, head(X), tail(X) >)
(SIGNATURES
    a__incr :: [A] -> A
    a__adx :: [A] -> A
    a__nats :: [] -> A
    a__zeros :: [] -> A
    a__head :: [A] -> A
    a__tail :: [A] -> A
    mark :: [A] -> A)
(RULES
    a__incr(nil()) -> nil()
    a__incr(cons(X,L)) ->
      cons(s(mark(X)),incr(L))
    a__adx(nil()) -> nil()
    a__adx(cons(X,L)) ->
      a__incr(cons(mark(X),adx(L)))
    a__nats() -> a__adx(a__zeros())
    a__zeros() -> cons(0(),zeros())
    a__head(cons(X,L)) -> mark(X)
    a__tail(cons(X,L)) -> mark(L)
    mark(incr(X)) ->
      a__incr(mark(X))
    mark(adx(X)) -> a__adx(mark(X))
    mark(nats()) -> a__nats()
    mark(zeros()) -> a__zeros()
    mark(head(X)) ->
      a__head(mark(X))
    mark(tail(X)) ->
      a__tail(mark(X))
    mark(nil()) -> nil()
    mark(cons(X1,X2)) ->
      cons(mark(X1),X2)
    mark(s(X)) -> s(mark(X))
    mark(0()) -> 0()
    a__incr(X) -> incr(X)
    a__adx(X) -> adx(X)
    a__nats() -> nats()
    a__zeros() -> zeros()
    a__head(X) -> head(X)
    a__tail(X) -> tail(X))