(STRATEGY
    INNERMOST)

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