WORST_CASE(?,O(n^2)) * Step 1: MI WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: bits(0()) -> 0() bits(s(x)) -> s(bits(half(s(x)))) half(0()) -> 0() half(s(0())) -> 0() half(s(s(x))) -> s(half(x)) - Signature: {bits/1,half/1} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {bits,half} and constructors {0,s} + Applied Processor: MI {miKind = Automaton Nothing, miDimension = 2, miUArgs = NoUArgs, miURules = NoURules, miSelector = Nothing} + Details: We apply a matrix interpretation of kind Automaton Nothing: Following symbols are considered usable: all TcT has computed the following interpretation: p(0) = [7] [2] p(bits) = [1 4] x_1 + [0] [1 4] [0] p(half) = [1 0] x_1 + [1] [1 0] [0] p(s) = [1 0] x_1 + [2] [1 0] [3] Following rules are strictly oriented: bits(0()) = [15] [15] > [7] [2] = 0() bits(s(x)) = [5 0] x + [14] [5 0] [14] > [5 0] x + [13] [5 0] [14] = s(bits(half(s(x)))) half(0()) = [8] [7] > [7] [2] = 0() half(s(0())) = [10] [9] > [7] [2] = 0() half(s(s(x))) = [1 0] x + [5] [1 0] [4] > [1 0] x + [3] [1 0] [4] = s(half(x)) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^2))