WORST_CASE(?,O(n^1)) * Step 1: NaturalPI 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: NaturalPI {shape = Linear, restrict = NoRestrict, uargs = UArgs, urules = URules, selector = Nothing} + Details: We apply a polynomial interpretation of kind constructor-based(linear): 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) = 9 + x1 + x2 p(False) = 5 p(Nil) = 8 p(True) = 7 p(even) = 7 + x1 p(evenodd) = 15 + 12*x1 p(notEmpty) = 12 p(odd) = 6 + x1 Following rules are strictly oriented: even(Cons(x,xs)) = 16 + x + xs > 6 + xs = odd(xs) even(Nil()) = 15 > 7 = True() evenodd(x) = 15 + 12*x > 7 + x = even(x) notEmpty(Cons(x,xs)) = 12 > 7 = True() notEmpty(Nil()) = 12 > 5 = False() odd(Cons(x,xs)) = 15 + x + xs > 7 + xs = even(xs) odd(Nil()) = 14 > 5 = False() Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))