(STRATEGY
    INNERMOST)

(VAR
    N X X1 X2 Y Z)
(DATATYPES
    A = µX.< cons(X, X), recip(X), terms(X), s(X), 0, nil, first(X, X), sqr(X), add(X, X), dbl(X) >)
(SIGNATURES
    a__terms :: [A] -> A
    a__sqr :: [A] -> A
    a__dbl :: [A] -> A
    a__add :: [A x A] -> A
    a__first :: [A x A] -> A
    mark :: [A] -> A)
(RULES
    a__terms(N) ->
      cons(recip(a__sqr(mark(N)))
          ,terms(s(N)))
    a__sqr(0()) -> 0()
    a__sqr(s(X)) ->
      s(a__add(a__sqr(mark(X))
              ,a__dbl(mark(X))))
    a__dbl(0()) -> 0()
    a__dbl(s(X)) ->
      s(s(a__dbl(mark(X))))
    a__add(0(),X) -> mark(X)
    a__add(s(X),Y) ->
      s(a__add(mark(X),mark(Y)))
    a__first(0(),X) -> nil()
    a__first(s(X),cons(Y,Z)) ->
      cons(mark(Y),first(X,Z))
    mark(terms(X)) ->
      a__terms(mark(X))
    mark(sqr(X)) -> a__sqr(mark(X))
    mark(add(X1,X2)) ->
      a__add(mark(X1),mark(X2))
    mark(dbl(X)) -> a__dbl(mark(X))
    mark(first(X1,X2)) ->
      a__first(mark(X1),mark(X2))
    mark(cons(X1,X2)) ->
      cons(mark(X1),X2)
    mark(recip(X)) -> recip(mark(X))
    mark(s(X)) -> s(mark(X))
    mark(0()) -> 0()
    mark(nil()) -> nil()
    a__terms(X) -> terms(X)
    a__sqr(X) -> sqr(X)
    a__add(X1,X2) -> add(X1,X2)
    a__dbl(X) -> dbl(X)
    a__first(X1,X2) -> first(X1,X2))