WORST_CASE(?,O(n^1)) * Step 1: NaturalPI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: div2(0()) -> 0() div2(S(0())) -> 0() div2(S(S(x))) -> +(S(0()),div2(x)) - Weak TRS: +(x,S(0())) -> S(x) +(S(0()),y) -> S(y) - Signature: {+/2,div2/1} / {0/0,S/1} - Obligation: innermost runtime complexity wrt. defined symbols {+,div2} 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: uargs(+) = {2} Following symbols are considered usable: {+,div2} TcT has computed the following interpretation: p(+) = x1 + x2 p(0) = 0 p(S) = 8 + x1 p(div2) = 2 + x1 Following rules are strictly oriented: div2(0()) = 2 > 0 = 0() div2(S(0())) = 10 > 0 = 0() div2(S(S(x))) = 18 + x > 10 + x = +(S(0()),div2(x)) Following rules are (at-least) weakly oriented: +(x,S(0())) = 8 + x >= 8 + x = S(x) +(S(0()),y) = 8 + y >= 8 + y = S(y) WORST_CASE(?,O(n^1))