MAYBE MAYBE TRS: { d(x, s(y), z) -> cond(ge(x, z), x, y, z), div(x, s(y)) -> d(x, s(y), 0()), cond(true(), x, y, z) -> s(d(x, s(y), plus(s(y), z))), cond(false(), x, y, z) -> 0(), ge(u, 0()) -> true(), ge(s(u), s(v)) -> ge(u, v), ge(0(), s(v)) -> false(), plus(n, s(m)) -> s(plus(n, m)), plus(n, 0()) -> n } DUP: We consider a duplicating system. Trs: { d(x, s(y), z) -> cond(ge(x, z), x, y, z), div(x, s(y)) -> d(x, s(y), 0()), cond(true(), x, y, z) -> s(d(x, s(y), plus(s(y), z))), cond(false(), x, y, z) -> 0(), ge(u, 0()) -> true(), ge(s(u), s(v)) -> ge(u, v), ge(0(), s(v)) -> false(), plus(n, s(m)) -> s(plus(n, m)), plus(n, 0()) -> n } Fail