Input TRS:
    1: active(nats()) -> mark(adx(zeros()))
    2: active(zeros()) -> mark(cons(0(),zeros()))
    3: active(incr(cons(X,Y))) -> mark(cons(s(X),incr(Y)))
    4: active(adx(cons(X,Y))) -> mark(incr(cons(X,adx(Y))))
    5: active(hd(cons(X,Y))) -> mark(X)
    6: active(tl(cons(X,Y))) -> mark(Y)
    7: active(adx(X)) -> adx(active(X))
    8: active(incr(X)) -> incr(active(X))
    9: active(hd(X)) -> hd(active(X))
    10: active(tl(X)) -> tl(active(X))
    11: adx(mark(X)) -> mark(adx(X))
    12: incr(mark(X)) -> mark(incr(X))
    13: hd(mark(X)) -> mark(hd(X))
    14: tl(mark(X)) -> mark(tl(X))
    15: proper(nats()) -> ok(nats())
    16: proper(adx(X)) -> adx(proper(X))
    17: proper(zeros()) -> ok(zeros())
    18: proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
    19: proper(0()) -> ok(0())
    20: proper(incr(X)) -> incr(proper(X))
    21: proper(s(X)) -> s(proper(X))
    22: proper(hd(X)) -> hd(proper(X))
    23: proper(tl(X)) -> tl(proper(X))
    24: adx(ok(X)) -> ok(adx(X))
    25: cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
    26: incr(ok(X)) -> ok(incr(X))
    27: s(ok(X)) -> ok(s(X))
    28: hd(ok(X)) -> ok(hd(X))
    29: tl(ok(X)) -> ok(tl(X))
    30: top(mark(X)) -> top(proper(X))
    31: top(ok(X)) -> top(active(X))
Number of Rules: 31
Direct QWPOS(Sum) ... failed.