(STRATEGY
    INNERMOST)

(VAR
    N X X1 X2 X3 X4 XS Y YS ZS)
(DATATYPES
    A = µX.< tt, pair(X, X), cons(X, X), natsFrom(X), s(X), 0, nil, U11(X, X, X, X), U12(X, X), splitAt(X, X), afterNth(X, X), snd(X), and(X, X), fst(X), head(X), sel(X, X), tail(X), take(X, X) >)
(SIGNATURES
    a__U11 :: [A x A x A x A] -> A
    a__U12 :: [A x A] -> A
    a__afterNth :: [A x A] -> A
    a__and :: [A x A] -> A
    a__fst :: [A] -> A
    a__head :: [A] -> A
    a__natsFrom :: [A] -> A
    a__sel :: [A x A] -> A
    a__snd :: [A] -> A
    a__splitAt :: [A x A] -> A
    a__tail :: [A] -> A
    a__take :: [A x A] -> A
    mark :: [A] -> A)
(RULES
    a__U11(tt(),N,X,XS) ->
      a__U12(a__splitAt(mark(N)
                       ,mark(XS))
            ,X)
    a__U12(pair(YS,ZS),X) ->
      pair(cons(mark(X),YS),mark(ZS))
    a__afterNth(N,XS) ->
      a__snd(a__splitAt(mark(N)
                       ,mark(XS)))
    a__and(tt(),X) -> mark(X)
    a__fst(pair(X,Y)) -> mark(X)
    a__head(cons(N,XS)) -> mark(N)
    a__natsFrom(N) -> cons(mark(N)
                          ,natsFrom(s(N)))
    a__sel(N,XS) ->
      a__head(a__afterNth(mark(N)
                         ,mark(XS)))
    a__snd(pair(X,Y)) -> mark(Y)
    a__splitAt(0(),XS) -> pair(nil()
                              ,mark(XS))
    a__splitAt(s(N),cons(X,XS)) ->
      a__U11(tt(),N,X,XS)
    a__tail(cons(N,XS)) -> mark(XS)
    a__take(N,XS) ->
      a__fst(a__splitAt(mark(N)
                       ,mark(XS)))
    mark(U11(X1,X2,X3,X4)) ->
      a__U11(mark(X1),X2,X3,X4)
    mark(U12(X1,X2)) ->
      a__U12(mark(X1),X2)
    mark(splitAt(X1,X2)) ->
      a__splitAt(mark(X1),mark(X2))
    mark(afterNth(X1,X2)) ->
      a__afterNth(mark(X1),mark(X2))
    mark(snd(X)) -> a__snd(mark(X))
    mark(and(X1,X2)) ->
      a__and(mark(X1),X2)
    mark(fst(X)) -> a__fst(mark(X))
    mark(head(X)) ->
      a__head(mark(X))
    mark(natsFrom(X)) ->
      a__natsFrom(mark(X))
    mark(sel(X1,X2)) ->
      a__sel(mark(X1),mark(X2))
    mark(tail(X)) ->
      a__tail(mark(X))
    mark(take(X1,X2)) ->
      a__take(mark(X1),mark(X2))
    mark(tt()) -> tt()
    mark(pair(X1,X2)) ->
      pair(mark(X1),mark(X2))
    mark(cons(X1,X2)) ->
      cons(mark(X1),X2)
    mark(s(X)) -> s(mark(X))
    mark(0()) -> 0()
    mark(nil()) -> nil()
    a__U11(X1,X2,X3,X4) -> U11(X1
                              ,X2
                              ,X3
                              ,X4)
    a__U12(X1,X2) -> U12(X1,X2)
    a__splitAt(X1,X2) -> splitAt(X1
                                ,X2)
    a__afterNth(X1,X2) ->
      afterNth(X1,X2)
    a__snd(X) -> snd(X)
    a__and(X1,X2) -> and(X1,X2)
    a__fst(X) -> fst(X)
    a__head(X) -> head(X)
    a__natsFrom(X) -> natsFrom(X)
    a__sel(X1,X2) -> sel(X1,X2)
    a__tail(X) -> tail(X)
    a__take(X1,X2) -> take(X1,X2))