WORST_CASE(?,O(n^1)) * Step 1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: average(x,s(s(s(y)))) -> s(average(s(x),y)) average(0(),0()) -> 0() average(0(),s(0())) -> 0() average(0(),s(s(0()))) -> s(0()) average(s(x),y) -> average(x,s(y)) - Signature: {average/2} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {average} and constructors {0,s} + 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: uargs(s) = {1} Following symbols are considered usable: {average} TcT has computed the following interpretation: p(0) = [0] p(average) = [12] x1 + [8] x2 + [6] p(s) = [1] x1 + [1] Following rules are strictly oriented: average(x,s(s(s(y)))) = [12] x + [8] y + [30] > [12] x + [8] y + [19] = s(average(s(x),y)) average(0(),0()) = [6] > [0] = 0() average(0(),s(0())) = [14] > [0] = 0() average(0(),s(s(0()))) = [22] > [1] = s(0()) average(s(x),y) = [12] x + [8] y + [18] > [12] x + [8] y + [14] = average(x,s(y)) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))