Input TRS:
    1: active(zeros()) -> mark(cons(0(),zeros()))
    2: active(and(tt(),X)) -> mark(X)
    3: active(length(nil())) -> mark(0())
    4: active(length(cons(N,L))) -> mark(s(length(L)))
    5: active(take(0(),IL)) -> mark(nil())
    6: active(take(s(M),cons(N,IL))) -> mark(cons(N,take(M,IL)))
    7: active(cons(X1,X2)) -> cons(active(X1),X2)
    8: active(and(X1,X2)) -> and(active(X1),X2)
    9: active(length(X)) -> length(active(X))
    10: active(s(X)) -> s(active(X))
    11: active(take(X1,X2)) -> take(active(X1),X2)
    12: active(take(X1,X2)) -> take(X1,active(X2))
    13: cons(mark(X1),X2) -> mark(cons(X1,X2))
    14: and(mark(X1),X2) -> mark(and(X1,X2))
    15: length(mark(X)) -> mark(length(X))
    16: s(mark(X)) -> mark(s(X))
    17: take(mark(X1),X2) -> mark(take(X1,X2))
    18: take(X1,mark(X2)) -> mark(take(X1,X2))
    19: proper(zeros()) -> ok(zeros())
    20: proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
    21: proper(0()) -> ok(0())
    22: proper(and(X1,X2)) -> and(proper(X1),proper(X2))
    23: proper(tt()) -> ok(tt())
    24: proper(length(X)) -> length(proper(X))
    25: proper(nil()) -> ok(nil())
    26: proper(s(X)) -> s(proper(X))
    27: proper(take(X1,X2)) -> take(proper(X1),proper(X2))
    28: cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
    29: and(ok(X1),ok(X2)) -> ok(and(X1,X2))
    30: length(ok(X)) -> ok(length(X))
    31: s(ok(X)) -> ok(s(X))
    32: take(ok(X1),ok(X2)) -> ok(take(X1,X2))
    33: top(mark(X)) -> top(proper(X))
    34: top(ok(X)) -> top(active(X))
Number of Rules: 34
Direct QWPOS(max) ... failed.