(STRATEGY
    INNERMOST)

(VAR
    X X1 X2 Y Z)
(DATATYPES
    A = µX.< true, false, 0, n__add(X, X), nil, cons(X, X), n__first(X, X), n__from(X), n__s(X) >)
(SIGNATURES
    and :: [A x A] -> A
    if :: [A x A x A] -> A
    add :: [A x A] -> A
    first :: [A x A] -> A
    from :: [A] -> A
    s :: [A] -> A
    activate :: [A] -> A)
(RULES
    and(true(),X) -> activate(X)
    and(false(),Y) -> false()
    if(true(),X,Y) -> activate(X)
    if(false(),X,Y) -> activate(Y)
    add(0(),X) -> activate(X)
    add(s(X),Y) ->
      s(n__add(activate(X)
              ,activate(Y)))
    first(0(),X) -> nil()
    first(s(X),cons(Y,Z)) ->
      cons(activate(Y)
          ,n__first(activate(X)
                   ,activate(Z)))
    from(X) -> cons(activate(X)
                   ,n__from(n__s(activate(X))))
    add(X1,X2) -> n__add(X1,X2)
    first(X1,X2) -> n__first(X1,X2)
    from(X) -> n__from(X)
    s(X) -> n__s(X)
    activate(n__add(X1,X2)) ->
      add(X1,X2)
    activate(n__first(X1,X2)) ->
      first(X1,X2)
    activate(n__from(X)) -> from(X)
    activate(n__s(X)) -> s(X)
    activate(X) -> X)