Input TRS:
    1: active(f(0())) -> mark(cons(0(),f(s(0()))))
    2: active(f(s(0()))) -> mark(f(p(s(0()))))
    3: active(p(s(X))) -> mark(X)
    4: active(f(X)) -> f(active(X))
    5: active(cons(X1,X2)) -> cons(active(X1),X2)
    6: active(s(X)) -> s(active(X))
    7: active(p(X)) -> p(active(X))
    8: f(mark(X)) -> mark(f(X))
    9: cons(mark(X1),X2) -> mark(cons(X1,X2))
    10: s(mark(X)) -> mark(s(X))
    11: p(mark(X)) -> mark(p(X))
    12: proper(f(X)) -> f(proper(X))
    13: proper(0()) -> ok(0())
    14: proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
    15: proper(s(X)) -> s(proper(X))
    16: proper(p(X)) -> p(proper(X))
    17: f(ok(X)) -> ok(f(X))
    18: cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
    19: s(ok(X)) -> ok(s(X))
    20: p(ok(X)) -> ok(p(X))
    21: top(mark(X)) -> top(proper(X))
    22: top(ok(X)) -> top(active(X))
Number of Rules: 22
Direct POLO(Sum) ... failed.