Input TRS:
    1: active(U11(tt(),M,N)) -> mark(U12(tt(),M,N))
    2: active(U12(tt(),M,N)) -> mark(s(plus(N,M)))
    3: active(plus(N,0())) -> mark(N)
    4: active(plus(N,s(M))) -> mark(U11(tt(),M,N))
    5: active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
    6: active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3)
    7: active(s(X)) -> s(active(X))
    8: active(plus(X1,X2)) -> plus(active(X1),X2)
    9: active(plus(X1,X2)) -> plus(X1,active(X2))
    10: U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3))
    11: U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3))
    12: s(mark(X)) -> mark(s(X))
    13: plus(mark(X1),X2) -> mark(plus(X1,X2))
    14: plus(X1,mark(X2)) -> mark(plus(X1,X2))
    15: proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3))
    16: proper(tt()) -> ok(tt())
    17: proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3))
    18: proper(s(X)) -> s(proper(X))
    19: proper(plus(X1,X2)) -> plus(proper(X1),proper(X2))
    20: proper(0()) -> ok(0())
    21: U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3))
    22: U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3))
    23: s(ok(X)) -> ok(s(X))
    24: plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
    25: top(mark(X)) -> top(proper(X))
    26: top(ok(X)) -> top(active(X))
Number of Rules: 26
Direct POLO(Sum) ... failed.