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(length(nil())) -> mark(0())
    5: active(length(cons(N,L))) -> mark(U11(tt(),L))
    6: active(cons(X1,X2)) -> cons(active(X1),X2)
    7: active(U11(X1,X2)) -> U11(active(X1),X2)
    8: active(U12(X1,X2)) -> U12(active(X1),X2)
    9: active(s(X)) -> s(active(X))
    10: active(length(X)) -> length(active(X))
    11: cons(mark(X1),X2) -> mark(cons(X1,X2))
    12: U11(mark(X1),X2) -> mark(U11(X1,X2))
    13: U12(mark(X1),X2) -> mark(U12(X1,X2))
    14: s(mark(X)) -> mark(s(X))
    15: length(mark(X)) -> mark(length(X))
    16: proper(zeros()) -> ok(zeros())
    17: proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
    18: proper(0()) -> ok(0())
    19: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
    20: proper(tt()) -> ok(tt())
    21: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
    22: proper(s(X)) -> s(proper(X))
    23: proper(length(X)) -> length(proper(X))
    24: proper(nil()) -> ok(nil())
    25: cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
    26: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
    27: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
    28: s(ok(X)) -> ok(s(X))
    29: length(ok(X)) -> ok(length(X))
    30: top(mark(X)) -> top(proper(X))
    31: top(ok(X)) -> top(active(X))
Number of Rules: 31
Direct POLO(mSum) ... failed.