(STRATEGY
    INNERMOST)

(VAR
    N X X1 X2 XS Y YS)
(DATATYPES
    A = µX.< cons(X, X), n__from(X), n__s(X), 0, nil, n__zWquot(X, X) >)
(SIGNATURES
    from :: [A] -> A
    sel :: [A x A] -> A
    minus :: [A x A] -> A
    quot :: [A x A] -> A
    zWquot :: [A x A] -> A
    s :: [A] -> A
    activate :: [A] -> A)
(RULES
    from(X) -> cons(X
                   ,n__from(n__s(X)))
    sel(0(),cons(X,XS)) -> X
    sel(s(N),cons(X,XS)) -> sel(N
                               ,activate(XS))
    minus(X,0()) -> 0()
    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)))
    zWquot(XS,nil()) -> nil()
    zWquot(nil(),XS) -> nil()
    zWquot(cons(X,XS),cons(Y,YS)) ->
      cons(quot(X,Y)
          ,n__zWquot(activate(XS)
                    ,activate(YS)))
    from(X) -> n__from(X)
    s(X) -> n__s(X)
    zWquot(X1,X2) -> n__zWquot(X1
                              ,X2)
    activate(n__from(X)) ->
      from(activate(X))
    activate(n__s(X)) ->
      s(activate(X))
    activate(n__zWquot(X1,X2)) ->
      zWquot(activate(X1)
            ,activate(X2))
    activate(X) -> X)