(STRATEGY
    INNERMOST)

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