(STRATEGY
    INNERMOST)

(VAR
    N X X1 X2 XS Y YS)
(DATATYPES
    A = µX.< cons(X, X), from(X), s(X), 0, nil, zWquot(X, X), sel(X, X), minus(X, X), quot(X, X) >)
(SIGNATURES
    a__from :: [A] -> A
    a__sel :: [A x A] -> A
    a__minus :: [A x A] -> A
    a__quot :: [A x A] -> A
    a__zWquot :: [A x A] -> A
    mark :: [A] -> A)
(RULES
    a__from(X) -> cons(mark(X)
                      ,from(s(X)))
    a__sel(0(),cons(X,XS)) ->
      mark(X)
    a__sel(s(N),cons(X,XS)) ->
      a__sel(mark(N),mark(XS))
    a__minus(X,0()) -> 0()
    a__minus(s(X),s(Y)) ->
      a__minus(mark(X),mark(Y))
    a__quot(0(),s(Y)) -> 0()
    a__quot(s(X),s(Y)) ->
      s(a__quot(a__minus(mark(X)
                        ,mark(Y))
               ,s(mark(Y))))
    a__zWquot(XS,nil()) -> nil()
    a__zWquot(nil(),XS) -> nil()
    a__zWquot(cons(X,XS)
             ,cons(Y,YS)) ->
      cons(a__quot(mark(X),mark(Y))
          ,zWquot(XS,YS))
    mark(from(X)) ->
      a__from(mark(X))
    mark(sel(X1,X2)) ->
      a__sel(mark(X1),mark(X2))
    mark(minus(X1,X2)) ->
      a__minus(mark(X1),mark(X2))
    mark(quot(X1,X2)) ->
      a__quot(mark(X1),mark(X2))
    mark(zWquot(X1,X2)) ->
      a__zWquot(mark(X1),mark(X2))
    mark(cons(X1,X2)) ->
      cons(mark(X1),X2)
    mark(s(X)) -> s(mark(X))
    mark(0()) -> 0()
    mark(nil()) -> nil()
    a__from(X) -> from(X)
    a__sel(X1,X2) -> sel(X1,X2)
    a__minus(X1,X2) -> minus(X1,X2)
    a__quot(X1,X2) -> quot(X1,X2)
    a__zWquot(X1,X2) -> zWquot(X1
                              ,X2))