(STRATEGY
    INNERMOST)

(VAR
    N X X1 X2 Y Z)
(DATATYPES
    A = µX.< n__from(X), s(X), 0, rnil, n__cons(X, X), rcons(X, X), posrecip(X), negrecip(X) >)
(SIGNATURES
    from :: [A] -> A
    2ndspos :: [A x A] -> A
    2ndsneg :: [A x A] -> A
    pi :: [A] -> A
    plus :: [A x A] -> A
    times :: [A x A] -> A
    square :: [A] -> A
    cons :: [A x A] -> A
    activate :: [A] -> A)
(RULES
    from(X) -> cons(X,n__from(s(X)))
    2ndspos(0(),Z) -> rnil()
    2ndspos(s(N)
           ,cons(X,n__cons(Y,Z))) ->
      rcons(posrecip(activate(Y))
           ,2ndsneg(N,activate(Z)))
    2ndsneg(0(),Z) -> rnil()
    2ndsneg(s(N)
           ,cons(X,n__cons(Y,Z))) ->
      rcons(negrecip(activate(Y))
           ,2ndspos(N,activate(Z)))
    pi(X) -> 2ndspos(X,from(0()))
    plus(0(),Y) -> Y
    plus(s(X),Y) -> s(plus(X,Y))
    times(0(),Y) -> 0()
    times(s(X),Y) -> plus(Y
                         ,times(X,Y))
    square(X) -> times(X,X)
    from(X) -> n__from(X)
    cons(X1,X2) -> n__cons(X1,X2)
    activate(n__from(X)) -> from(X)
    activate(n__cons(X1,X2)) ->
      cons(X1,X2)
    activate(X) -> X)