MAYBE MAYBE TRS: { cond(true(), x, y) -> s(minus(x, s(y))), equal(s(x), s(y)) -> equal(x, y), equal(s(x), 0()) -> false(), equal(0(), s(y)) -> false(), equal(0(), 0()) -> true(), min(u, 0()) -> 0(), min(s(u), s(v)) -> s(min(u, v)), min(0(), v) -> 0(), minus(x, y) -> cond(equal(min(x, y), y), x, y) } DUP: We consider a duplicating system. Trs: { cond(true(), x, y) -> s(minus(x, s(y))), equal(s(x), s(y)) -> equal(x, y), equal(s(x), 0()) -> false(), equal(0(), s(y)) -> false(), equal(0(), 0()) -> true(), min(u, 0()) -> 0(), min(s(u), s(v)) -> s(min(u, v)), min(0(), v) -> 0(), minus(x, y) -> cond(equal(min(x, y), y), x, y) } Fail