(STRATEGY
    INNERMOST)

(VAR
    N X Y Z)
(DATATYPES
    A = µX.< cons(X, X), s(X), 0, rnil, cons2(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)
(RULES
    from(X) -> cons(X,from(s(X)))
    2ndspos(0(),Z) -> rnil()
    2ndspos(s(N),cons(X,Z)) ->
      2ndspos(s(N),cons2(X,Z))
    2ndspos(s(N)
           ,cons2(X,cons(Y,Z))) ->
      rcons(posrecip(Y),2ndsneg(N,Z))
    2ndsneg(0(),Z) -> rnil()
    2ndsneg(s(N),cons(X,Z)) ->
      2ndsneg(s(N),cons2(X,Z))
    2ndsneg(s(N)
           ,cons2(X,cons(Y,Z))) ->
      rcons(negrecip(Y),2ndspos(N,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))