Input TRS:
    1: active(nats()) -> mark(cons(0(),incr(nats())))
    2: active(pairs()) -> mark(cons(0(),incr(odds())))
    3: active(odds()) -> mark(incr(pairs()))
    4: active(incr(cons(X,XS))) -> mark(cons(s(X),incr(XS)))
    5: active(head(cons(X,XS))) -> mark(X)
    6: active(tail(cons(X,XS))) -> mark(XS)
    7: active(cons(X1,X2)) -> cons(active(X1),X2)
    8: active(incr(X)) -> incr(active(X))
    9: active(s(X)) -> s(active(X))
    10: active(head(X)) -> head(active(X))
    11: active(tail(X)) -> tail(active(X))
    12: cons(mark(X1),X2) -> mark(cons(X1,X2))
    13: incr(mark(X)) -> mark(incr(X))
    14: s(mark(X)) -> mark(s(X))
    15: head(mark(X)) -> mark(head(X))
    16: tail(mark(X)) -> mark(tail(X))
    17: proper(nats()) -> ok(nats())
    18: proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
    19: proper(0()) -> ok(0())
    20: proper(incr(X)) -> incr(proper(X))
    21: proper(pairs()) -> ok(pairs())
    22: proper(odds()) -> ok(odds())
    23: proper(s(X)) -> s(proper(X))
    24: proper(head(X)) -> head(proper(X))
    25: proper(tail(X)) -> tail(proper(X))
    26: cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
    27: incr(ok(X)) -> ok(incr(X))
    28: s(ok(X)) -> ok(s(X))
    29: head(ok(X)) -> ok(head(X))
    30: tail(ok(X)) -> ok(tail(X))
    31: top(mark(X)) -> top(proper(X))
    32: top(ok(X)) -> top(active(X))
Number of Rules: 32
Direct QLPOS ... failed.