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(cons(X1,X2)) -> cons(active(X1),X2)
    6: active(and(X1,X2)) -> and(active(X1),X2)
    7: active(length(X)) -> length(active(X))
    8: active(s(X)) -> s(active(X))
    9: cons(mark(X1),X2) -> mark(cons(X1,X2))
    10: and(mark(X1),X2) -> mark(and(X1,X2))
    11: length(mark(X)) -> mark(length(X))
    12: s(mark(X)) -> mark(s(X))
    13: proper(zeros()) -> ok(zeros())
    14: proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
    15: proper(0()) -> ok(0())
    16: proper(and(X1,X2)) -> and(proper(X1),proper(X2))
    17: proper(tt()) -> ok(tt())
    18: proper(length(X)) -> length(proper(X))
    19: proper(nil()) -> ok(nil())
    20: proper(s(X)) -> s(proper(X))
    21: cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
    22: and(ok(X1),ok(X2)) -> ok(and(X1,X2))
    23: length(ok(X)) -> ok(length(X))
    24: s(ok(X)) -> ok(s(X))
    25: top(mark(X)) -> top(proper(X))
    26: top(ok(X)) -> top(active(X))
Number of Rules: 26
Direct POLO(Sum) ... removes: 3 2
	I(tt) = 1
	I(mark) = x1
	I(active) = x1
	I(0) = 0
	I(top) = x1
	I(nil) = 0
	I(and) = x1 + x2
	I(s) = x1
	I(length) = x1 + 1
	I(zeros) = 0
	I(cons) = x1 + x2
	I(ok) = x1
	I(proper) = x1
Number of Rules: 24
Direct POLO(Sum) ...Direct QLPOS ...Direct QKBOS ... failed.