(STRATEGY
    INNERMOST)

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