(STRATEGY
    INNERMOST)

(VAR
    M N X X1 X2)
(DATATYPES
    A = µX.< tt, mark(X), 0, ok(X) >)
(SIGNATURES
    active :: [A] -> A
    and :: [A x A] -> A
    plus :: [A x A] -> A
    s :: [A] -> A
    x :: [A x A] -> A
    proper :: [A] -> A
    top :: [A] -> A)
(RULES
    active(and(tt(),X)) -> mark(X)
    active(plus(N,0())) -> mark(N)
    active(plus(N,s(M))) ->
      mark(s(plus(N,M)))
    active(x(N,0())) -> mark(0())
    active(x(N,s(M))) ->
      mark(plus(x(N,M),N))
    active(and(X1,X2)) ->
      and(active(X1),X2)
    active(plus(X1,X2)) ->
      plus(active(X1),X2)
    active(plus(X1,X2)) -> plus(X1
                               ,active(X2))
    active(s(X)) -> s(active(X))
    active(x(X1,X2)) -> x(active(X1)
                         ,X2)
    active(x(X1,X2)) -> x(X1
                         ,active(X2))
    and(mark(X1),X2) -> mark(and(X1
                                ,X2))
    plus(mark(X1),X2) ->
      mark(plus(X1,X2))
    plus(X1,mark(X2)) ->
      mark(plus(X1,X2))
    s(mark(X)) -> mark(s(X))
    x(mark(X1),X2) -> mark(x(X1,X2))
    x(X1,mark(X2)) -> mark(x(X1,X2))
    proper(and(X1,X2)) ->
      and(proper(X1),proper(X2))
    proper(tt()) -> ok(tt())
    proper(plus(X1,X2)) ->
      plus(proper(X1),proper(X2))
    proper(0()) -> ok(0())
    proper(s(X)) -> s(proper(X))
    proper(x(X1,X2)) -> x(proper(X1)
                         ,proper(X2))
    and(ok(X1),ok(X2)) -> ok(and(X1
                                ,X2))
    plus(ok(X1),ok(X2)) ->
      ok(plus(X1,X2))
    s(ok(X)) -> ok(s(X))
    x(ok(X1),ok(X2)) -> ok(x(X1,X2))
    top(mark(X)) -> top(proper(X))
    top(ok(X)) -> top(active(X)))