WORST_CASE(?,O(n^1)) * Step 1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: even(Cons(x,xs)) -> odd(xs) even(Nil()) -> True() evenodd(x) -> even(x) notEmpty(Cons(x,xs)) -> True() notEmpty(Nil()) -> False() odd(Cons(x,xs)) -> even(xs) odd(Nil()) -> False() - Signature: {even/1,evenodd/1,notEmpty/1,odd/1} / {Cons/2,False/0,Nil/0,True/0} - Obligation: innermost runtime complexity wrt. defined symbols {even,evenodd,notEmpty,odd} and constructors {Cons,False ,Nil,True} + Applied Processor: NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing} + Details: We apply a matrix interpretation of kind constructor based matrix interpretation: The following argument positions are considered usable: none Following symbols are considered usable: {even,evenodd,notEmpty,odd} TcT has computed the following interpretation: p(Cons) = [1] x1 + [1] x2 + [1] p(False) = [2] p(Nil) = [6] p(True) = [4] p(even) = [1] x1 + [0] p(evenodd) = [1] x1 + [8] p(notEmpty) = [2] x1 + [9] p(odd) = [1] x1 + [0] Following rules are strictly oriented: even(Cons(x,xs)) = [1] x + [1] xs + [1] > [1] xs + [0] = odd(xs) even(Nil()) = [6] > [4] = True() evenodd(x) = [1] x + [8] > [1] x + [0] = even(x) notEmpty(Cons(x,xs)) = [2] x + [2] xs + [11] > [4] = True() notEmpty(Nil()) = [21] > [2] = False() odd(Cons(x,xs)) = [1] x + [1] xs + [1] > [1] xs + [0] = even(xs) odd(Nil()) = [6] > [2] = False() Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))