2.06/1.03 YES 2.06/1.03 2.06/1.03 Problem: 2.06/1.03 lte(0(), n) -> true() 2.06/1.03 lte(s(m), 0()) -> false() 2.06/1.03 lte(s(m), s(n)) -> lte(m, n) 2.06/1.03 insert(nil(), m) -> cons(m, nil()) 2.06/1.03 insert(cons(n, l), m) -> cons(m, cons(n, l)) <= lte(m, n) = true() 2.06/1.03 insert(cons(n, l), m) -> cons(n, insert(l, m)) <= lte(m, n) = false() 2.06/1.04 ordered(nil()) -> true() 2.06/1.04 ordered(cons(m, nil())) -> true() 2.06/1.04 ordered(cons(m, cons(n, l))) -> ordered(cons(n, l)) <= lte(m, n) = true() 2.06/1.04 ordered(cons(m, cons(n, l))) -> false() <= lte(m, n) = false() 2.06/1.04 2.06/1.04 Proof: 2.06/1.04 This system is confluent. 2.06/1.04 By \cite{GNG13}, Theorem 9. 2.06/1.04 This system is of type 3 or smaller. 2.06/1.04 This system is deterministic. 2.06/1.04 This system is weakly left-linear. 2.06/1.04 System R transformed to optimized U(R). 2.06/1.04 This system is orthogonal. 2.06/1.04 2.66/1.34 EOF