Input TRS:
    1: active(and(tt(),X)) -> mark(X)
    2: active(plus(N,0())) -> mark(N)
    3: active(plus(N,s(M))) -> mark(s(plus(N,M)))
    4: active(and(X1,X2)) -> and(active(X1),X2)
    5: active(plus(X1,X2)) -> plus(active(X1),X2)
    6: active(plus(X1,X2)) -> plus(X1,active(X2))
    7: active(s(X)) -> s(active(X))
    8: and(mark(X1),X2) -> mark(and(X1,X2))
    9: plus(mark(X1),X2) -> mark(plus(X1,X2))
    10: plus(X1,mark(X2)) -> mark(plus(X1,X2))
    11: s(mark(X)) -> mark(s(X))
    12: proper(and(X1,X2)) -> and(proper(X1),proper(X2))
    13: proper(tt()) -> ok(tt())
    14: proper(plus(X1,X2)) -> plus(proper(X1),proper(X2))
    15: proper(0()) -> ok(0())
    16: proper(s(X)) -> s(proper(X))
    17: and(ok(X1),ok(X2)) -> ok(and(X1,X2))
    18: plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
    19: s(ok(X)) -> ok(s(X))
    20: top(mark(X)) -> top(proper(X))
    21: top(ok(X)) -> top(active(X))
Number of Rules: 21
Direct QTKBOS ... failed.