0.85/1.36 YES 0.85/1.36 0.85/1.36 Problem: 0.85/1.36 lte(0(), n) -> true() 0.85/1.36 lte(s(m), 0()) -> false() 0.85/1.36 lte(s(m), s(n)) -> lte(m, n) 0.85/1.36 insert(nil(), m) -> cons(m, nil()) 0.85/1.36 insert(cons(n, l), m) -> cons(m, cons(n, l)) <= lte(m, n) = true() 0.85/1.36 insert(cons(n, l), m) -> cons(n, insert(l, m)) <= lte(m, n) = false() 0.85/1.36 ordered(nil()) -> true() 0.85/1.36 ordered(cons(m, nil())) -> true() 0.85/1.36 ordered(cons(m, cons(n, l))) -> ordered(cons(n, l)) <= lte(m, n) = true() 0.85/1.36 ordered(cons(m, cons(n, l))) -> false() <= lte(m, n) = false() 0.85/1.36 0.85/1.36 Proof: 0.85/1.36 This system is confluent. 0.85/1.36 By \cite{GNG13}, Theorem 9. 0.85/1.36 This system is of type 3 or smaller. 0.85/1.36 This system is deterministic. 0.85/1.36 This system is weakly left-linear. 0.85/1.36 System R transformed to optimized U(R). 0.85/1.36 This system is orthogonal. 0.85/1.36 0.93/1.65 EOF