(STRATEGY
    INNERMOST)

(VAR
    n x y z)
(DATATYPES
    A = µX.< nil, true, add(X, X), false >)
(SIGNATURES
    null :: [A] -> A
    tail :: [A] -> A
    head :: [A] -> A
    app :: [A x A] -> A
    reverse :: [A] -> A
    shuffle :: [A] -> A
    shuff :: [A x A] -> A
    if :: [A x A x A x A] -> A)
(RULES
    null(nil()) -> true()
    null(add(n,x)) -> false()
    tail(add(n,x)) -> x
    tail(nil()) -> nil()
    head(add(n,x)) -> n
    app(nil(),y) -> y
    app(add(n,x),y) -> add(n
                          ,app(x,y))
    reverse(nil()) -> nil()
    reverse(add(n,x)) ->
      app(reverse(x),add(n,nil()))
    shuffle(x) -> shuff(x,nil())
    shuff(x,y) -> if(null(x)
                    ,x
                    ,y
                    ,app(y,add(head(x),nil())))
    if(true(),x,y,z) -> y
    if(false(),x,y,z) ->
      shuff(reverse(tail(x)),z))