WORST_CASE(?,O(n^1)) * Step 1: NaturalPI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: even(0()) -> S(0()) even(S(x)) -> odd(x) odd(0()) -> 0() odd(S(x)) -> even(x) - Signature: {even/1,odd/1} / {0/0,S/1} - Obligation: innermost runtime complexity wrt. defined symbols {even,odd} and constructors {0,S} + Applied Processor: NaturalPI {shape = StronglyLinear, restrict = NoRestrict, uargs = UArgs, urules = URules, selector = Nothing} + Details: We apply a polynomial interpretation of kind constructor-based(stronglyLinear): The following argument positions are considered usable: none Following symbols are considered usable: {even,odd} TcT has computed the following interpretation: p(0) = 0 p(S) = 1 + x1 p(even) = 2 + x1 p(odd) = 2 + x1 Following rules are strictly oriented: even(0()) = 2 > 1 = S(0()) even(S(x)) = 3 + x > 2 + x = odd(x) odd(0()) = 2 > 0 = 0() odd(S(x)) = 3 + x > 2 + x = even(x) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))