(STRATEGY
    INNERMOST)

(VAR
    X X1 X2 XS)
(DATATYPES
    A = µX.< cons(X, X), 0, incr(X), nats, odds, s(X), pairs, head(X), tail(X), nil >)
(SIGNATURES
    a__nats :: [] -> A
    a__pairs :: [] -> A
    a__odds :: [] -> A
    a__incr :: [A] -> A
    a__head :: [A] -> A
    a__tail :: [A] -> A
    mark :: [A] -> A)
(RULES
    a__nats() -> cons(0()
                     ,incr(nats()))
    a__pairs() -> cons(0()
                      ,incr(odds()))
    a__odds() -> a__incr(a__pairs())
    a__incr(cons(X,XS)) ->
      cons(s(mark(X)),incr(XS))
    a__head(cons(X,XS)) -> mark(X)
    a__tail(cons(X,XS)) -> mark(XS)
    mark(nats()) -> a__nats()
    mark(pairs()) -> a__pairs()
    mark(odds()) -> a__odds()
    mark(incr(X)) ->
      a__incr(mark(X))
    mark(head(X)) ->
      a__head(mark(X))
    mark(tail(X)) ->
      a__tail(mark(X))
    mark(0()) -> 0()
    mark(s(X)) -> s(mark(X))
    mark(nil()) -> nil()
    mark(cons(X1,X2)) ->
      cons(mark(X1),X2)
    a__nats() -> nats()
    a__pairs() -> pairs()
    a__odds() -> odds()
    a__incr(X) -> incr(X)
    a__head(X) -> head(X)
    a__tail(X) -> tail(X))