(STRATEGY
    INNERMOST)

(VAR
    x xs y)
(DATATYPES
    A = µX.< 0, s(X), nil, cons(X, X) >)
(SIGNATURES
    sub :: [A x A] -> A
    zero :: [A] -> A
    zero2 :: [A x A] -> A)
(RULES
    sub(0(),0()) -> 0()
    sub(s(x),0()) -> s(x)
    sub(0(),s(x)) -> 0()
    sub(s(x),s(y)) -> sub(x,y)
    zero(nil()) -> zero2(0(),nil())
    zero(cons(x,xs)) -> zero2(sub(x
                                 ,x)
                             ,cons(x,xs))
    zero2(0(),nil()) -> nil()
    zero2(0(),cons(x,xs)) ->
      cons(sub(x,x),zero(xs))
    zero2(s(y),nil()) -> zero(nil())
    zero2(s(y),cons(x,xs)) ->
      zero(cons(x,xs)))