(STRATEGY
    INNERMOST)

(VAR
    N X X1 X2 XS Y)
(DATATYPES
    A = µX.< s(X), 0, cons(X, X), fib1(X, X), add(X, X), fib(X), sel(X, X) >)
(SIGNATURES
    a__fib :: [A] -> A
    a__fib1 :: [A x A] -> A
    a__add :: [A x A] -> A
    a__sel :: [A x A] -> A
    mark :: [A] -> A)
(RULES
    a__fib(N) -> a__sel(mark(N)
                       ,a__fib1(s(0()),s(0())))
    a__fib1(X,Y) -> cons(mark(X)
                        ,fib1(Y,add(X,Y)))
    a__add(0(),X) -> mark(X)
    a__add(s(X),Y) ->
      s(a__add(mark(X),mark(Y)))
    a__sel(0(),cons(X,XS)) ->
      mark(X)
    a__sel(s(N),cons(X,XS)) ->
      a__sel(mark(N),mark(XS))
    mark(fib(X)) -> a__fib(mark(X))
    mark(sel(X1,X2)) ->
      a__sel(mark(X1),mark(X2))
    mark(fib1(X1,X2)) ->
      a__fib1(mark(X1),mark(X2))
    mark(add(X1,X2)) ->
      a__add(mark(X1),mark(X2))
    mark(s(X)) -> s(mark(X))
    mark(0()) -> 0()
    mark(cons(X1,X2)) ->
      cons(mark(X1),X2)
    a__fib(X) -> fib(X)
    a__sel(X1,X2) -> sel(X1,X2)
    a__fib1(X1,X2) -> fib1(X1,X2)
    a__add(X1,X2) -> add(X1,X2))