(STRATEGY
    INNERMOST)

(VAR
    L N X X1 X2)
(DATATYPES
    A = µX.< zeros, mark(X), 0, tt, nil, ok(X) >)
(SIGNATURES
    active :: [A] -> A
    cons :: [A x A] -> A
    U11 :: [A x A] -> A
    U12 :: [A x A] -> A
    s :: [A] -> A
    length :: [A] -> A
    proper :: [A] -> A
    top :: [A] -> A)
(RULES
    active(zeros()) -> mark(cons(0()
                                ,zeros()))
    active(U11(tt(),L)) ->
      mark(U12(tt(),L))
    active(U12(tt(),L)) ->
      mark(s(length(L)))
    active(length(nil())) ->
      mark(0())
    active(length(cons(N,L))) ->
      mark(U11(tt(),L))
    active(cons(X1,X2)) ->
      cons(active(X1),X2)
    active(U11(X1,X2)) ->
      U11(active(X1),X2)
    active(U12(X1,X2)) ->
      U12(active(X1),X2)
    active(s(X)) -> s(active(X))
    active(length(X)) ->
      length(active(X))
    cons(mark(X1),X2) ->
      mark(cons(X1,X2))
    U11(mark(X1),X2) -> mark(U11(X1
                                ,X2))
    U12(mark(X1),X2) -> mark(U12(X1
                                ,X2))
    s(mark(X)) -> mark(s(X))
    length(mark(X)) ->
      mark(length(X))
    proper(zeros()) -> ok(zeros())
    proper(cons(X1,X2)) ->
      cons(proper(X1),proper(X2))
    proper(0()) -> ok(0())
    proper(U11(X1,X2)) ->
      U11(proper(X1),proper(X2))
    proper(tt()) -> ok(tt())
    proper(U12(X1,X2)) ->
      U12(proper(X1),proper(X2))
    proper(s(X)) -> s(proper(X))
    proper(length(X)) ->
      length(proper(X))
    proper(nil()) -> ok(nil())
    cons(ok(X1),ok(X2)) ->
      ok(cons(X1,X2))
    U11(ok(X1),ok(X2)) -> ok(U11(X1
                                ,X2))
    U12(ok(X1),ok(X2)) -> ok(U12(X1
                                ,X2))
    s(ok(X)) -> ok(s(X))
    length(ok(X)) -> ok(length(X))
    top(mark(X)) -> top(proper(X))
    top(ok(X)) -> top(active(X)))