Input TRS:
    1: active(zeros()) -> mark(cons(0(),zeros()))
    2: active(U11(tt(),L)) -> mark(U12(tt(),L))
    3: active(U12(tt(),L)) -> mark(s(length(L)))
    4: active(U21(tt(),IL,M,N)) -> mark(U22(tt(),IL,M,N))
    5: active(U22(tt(),IL,M,N)) -> mark(U23(tt(),IL,M,N))
    6: active(U23(tt(),IL,M,N)) -> mark(cons(N,take(M,IL)))
    7: active(length(nil())) -> mark(0())
    8: active(length(cons(N,L))) -> mark(U11(tt(),L))
    9: active(take(0(),IL)) -> mark(nil())
    10: active(take(s(M),cons(N,IL))) -> mark(U21(tt(),IL,M,N))
    11: active(cons(X1,X2)) -> cons(active(X1),X2)
    12: active(U11(X1,X2)) -> U11(active(X1),X2)
    13: active(U12(X1,X2)) -> U12(active(X1),X2)
    14: active(s(X)) -> s(active(X))
    15: active(length(X)) -> length(active(X))
    16: active(U21(X1,X2,X3,X4)) -> U21(active(X1),X2,X3,X4)
    17: active(U22(X1,X2,X3,X4)) -> U22(active(X1),X2,X3,X4)
    18: active(U23(X1,X2,X3,X4)) -> U23(active(X1),X2,X3,X4)
    19: active(take(X1,X2)) -> take(active(X1),X2)
    20: active(take(X1,X2)) -> take(X1,active(X2))
    21: cons(mark(X1),X2) -> mark(cons(X1,X2))
    22: U11(mark(X1),X2) -> mark(U11(X1,X2))
    23: U12(mark(X1),X2) -> mark(U12(X1,X2))
    24: s(mark(X)) -> mark(s(X))
    25: length(mark(X)) -> mark(length(X))
    26: U21(mark(X1),X2,X3,X4) -> mark(U21(X1,X2,X3,X4))
    27: U22(mark(X1),X2,X3,X4) -> mark(U22(X1,X2,X3,X4))
    28: U23(mark(X1),X2,X3,X4) -> mark(U23(X1,X2,X3,X4))
    29: take(mark(X1),X2) -> mark(take(X1,X2))
    30: take(X1,mark(X2)) -> mark(take(X1,X2))
    31: proper(zeros()) -> ok(zeros())
    32: proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
    33: proper(0()) -> ok(0())
    34: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
    35: proper(tt()) -> ok(tt())
    36: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
    37: proper(s(X)) -> s(proper(X))
    38: proper(length(X)) -> length(proper(X))
    39: proper(U21(X1,X2,X3,X4)) -> U21(proper(X1),proper(X2),proper(X3),proper(X4))
    40: proper(U22(X1,X2,X3,X4)) -> U22(proper(X1),proper(X2),proper(X3),proper(X4))
    41: proper(U23(X1,X2,X3,X4)) -> U23(proper(X1),proper(X2),proper(X3),proper(X4))
    42: proper(take(X1,X2)) -> take(proper(X1),proper(X2))
    43: proper(nil()) -> ok(nil())
    44: cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
    45: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
    46: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
    47: s(ok(X)) -> ok(s(X))
    48: length(ok(X)) -> ok(length(X))
    49: U21(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U21(X1,X2,X3,X4))
    50: U22(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U22(X1,X2,X3,X4))
    51: U23(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U23(X1,X2,X3,X4))
    52: take(ok(X1),ok(X2)) -> ok(take(X1,X2))
    53: top(mark(X)) -> top(proper(X))
    54: top(ok(X)) -> top(active(X))
Number of Rules: 54
Direct QKBOS(Sum) ... failed.