1.33/1.61 YES 1.33/1.61 1.33/1.61 Problem: 1.33/1.61 fstsplit(0(), x) -> nil() 1.33/1.61 fstsplit(s(n), nil()) -> nil() 1.33/1.61 fstsplit(s(n), cons(h, t)) -> cons(h, fstsplit(n, t)) 1.33/1.61 sndsplit(0(), x) -> x 1.33/1.61 sndsplit(s(n), nil()) -> nil() 1.33/1.61 sndsplit(s(n), cons(h, t)) -> sndsplit(n, t) 1.33/1.61 empty(nil()) -> true() 1.33/1.61 empty(cons(h, t)) -> false() 1.33/1.61 leq(0(), m) -> true() 1.33/1.61 leq(s(n), 0()) -> false() 1.33/1.61 leq(s(n), s(m)) -> leq(n, m) 1.33/1.61 length(nil()) -> 0() 1.33/1.61 length(cons(h, t)) -> s(length(t)) 1.33/1.61 app(nil(), x) -> x 1.33/1.61 app(cons(h, t), x) -> cons(h, app(t, x)) 1.33/1.61 map_f(pid, nil()) -> nil() 1.33/1.61 map_f(pid, cons(h, t)) -> app(f(pid, h), map_f(pid, t)) 1.33/1.61 process(store, m) -> process(app(map_f(self(), nil()), sndsplit(m, store)), m) <= leq(m, length(store)) = true(), empty(fstsplit(m, store)) = false() 1.33/1.61 process(store, m) -> process(sndsplit(m, app(map_f(self(), nil()), store)), m) <= leq(m, length(store)) = false(), empty(fstsplit(m, app(map_f(self(), nil()), store))) = false() 1.33/1.61 1.33/1.61 Proof: 1.33/1.61 This system is confluent. 1.33/1.61 By \cite{GNG13}, Theorem 9. 1.33/1.61 This system is of type 3 or smaller. 1.33/1.61 This system is deterministic. 1.33/1.61 This system is weakly left-linear. 1.33/1.61 System R transformed to optimized U(R). 1.33/1.61 This system is orthogonal. 1.33/1.61 1.34/1.93 EOF