(STRATEGY
    INNERMOST)

(VAR
    X X1 X2 X3 Y Z)
(DATATYPES
    A = µX.< true, false, 0, s(X), add(X, X), nil, cons(X, X), first(X, X), from(X), and(X, X), if(X, X, X) >)
(SIGNATURES
    a__and :: [A x A] -> A
    a__if :: [A x A x A] -> A
    a__add :: [A x A] -> A
    a__first :: [A x A] -> A
    a__from :: [A] -> A
    mark :: [A] -> A)
(RULES
    a__and(true(),X) -> mark(X)
    a__and(false(),Y) -> false()
    a__if(true(),X,Y) -> mark(X)
    a__if(false(),X,Y) -> mark(Y)
    a__add(0(),X) -> mark(X)
    a__add(s(X),Y) -> s(add(X,Y))
    a__first(0(),X) -> nil()
    a__first(s(X),cons(Y,Z)) ->
      cons(Y,first(X,Z))
    a__from(X) -> cons(X,from(s(X)))
    mark(and(X1,X2)) ->
      a__and(mark(X1),X2)
    mark(if(X1,X2,X3)) ->
      a__if(mark(X1),X2,X3)
    mark(add(X1,X2)) ->
      a__add(mark(X1),X2)
    mark(first(X1,X2)) ->
      a__first(mark(X1),mark(X2))
    mark(from(X)) -> a__from(X)
    mark(true()) -> true()
    mark(false()) -> false()
    mark(0()) -> 0()
    mark(s(X)) -> s(X)
    mark(nil()) -> nil()
    mark(cons(X1,X2)) -> cons(X1,X2)
    a__and(X1,X2) -> and(X1,X2)
    a__if(X1,X2,X3) -> if(X1,X2,X3)
    a__add(X1,X2) -> add(X1,X2)
    a__first(X1,X2) -> first(X1,X2)
    a__from(X) -> from(X))