WORST_CASE(?,O(n^1)) * Step 1: NaturalPI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: b(r(x)) -> r(b(x)) b(w(x)) -> w(b(x)) w(r(x)) -> r(w(x)) - Signature: {b/1,w/1} / {r/1} - Obligation: innermost runtime complexity wrt. defined symbols {b,w} and constructors {r} + 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: uargs(r) = {1}, uargs(w) = {1} Following symbols are considered usable: {b,w} TcT has computed the following interpretation: p(b) = 3 + 8*x1 p(r) = 3 + x1 p(w) = 3 + 2*x1 Following rules are strictly oriented: b(r(x)) = 27 + 8*x > 6 + 8*x = r(b(x)) b(w(x)) = 27 + 16*x > 9 + 16*x = w(b(x)) w(r(x)) = 9 + 2*x > 6 + 2*x = r(w(x)) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))