0.00/0.48 MAYBE 0.00/0.48 0.00/0.48 Problem: 0.00/0.48 eq(0(), 0()) -> true() 0.00/0.48 eq(s(x), 0()) -> false() 0.00/0.48 eq(0(), s(y)) -> false() 0.00/0.48 eq(s(x), s(y)) -> eq(x, y) 0.00/0.48 lte(0(), y) -> true() 0.00/0.48 lte(s(x), 0()) -> false() 0.00/0.48 lte(s(x), s(y)) -> lte(x, y) 0.00/0.48 m(0(), s(y)) -> 0() 0.00/0.48 m(x, 0()) -> x 0.00/0.48 m(s(x), s(y)) -> m(x, y) 0.00/0.48 mod(0(), y) -> 0() 0.00/0.48 mod(s(x), 0()) -> 0() 0.00/0.49 mod(s(x), s(y)) -> mod(m(x, y), s(y)) <= lte(y, x) = true() 0.00/0.49 mod(s(x), s(y)) -> s(x) <= lte(y, x) = false() 0.00/0.49 filter(n, r, nil()) -> nil() 0.00/0.49 filter(n, r, cons(x, xs)) -> cons(x, filter(n, r, xs)) <= mod(x, n) = r', eq(r, r') = true() 0.00/0.49 filter(n, r, cons(x, xs)) -> filter(n, r, xs) <= mod(x, n) = n', eq(r, r') = false() 0.00/0.49 0.00/0.49 Proof: 0.00/0.49 ConCon could not decide confluence of the system. 0.00/0.49 \cite{ALS94}, Theorem 4.1 does not apply. 0.00/0.49 This system may be strongly deterministic or not. 0.00/0.49 0.00/0.50 EOF