(STRATEGY
    INNERMOST)

(VAR
    k l x y)
(DATATYPES
    A = µX.< nil, cons(X, X), 0, s(X) >)
(SIGNATURES
    app :: [A x A] -> A
    sum :: [A] -> A
    plus :: [A x A] -> A
    pred :: [A] -> A)
(RULES
    app(nil(),k) -> k
    app(l,nil()) -> l
    app(cons(x,l),k) -> cons(x
                            ,app(l,k))
    sum(cons(x,nil())) -> cons(x
                              ,nil())
    sum(cons(x,cons(y,l))) ->
      sum(cons(plus(x,y),l))
    sum(app(l,cons(x,cons(y,k)))) ->
      sum(app(l
             ,sum(cons(x,cons(y,k)))))
    plus(0(),y) -> y
    plus(s(x),y) -> s(plus(x,y))
    sum(plus(cons(0(),x)
            ,cons(y,l))) ->
      pred(sum(cons(s(x),cons(y,l))))
    pred(cons(s(x),nil())) -> cons(x
                                  ,nil()))