WORST_CASE(?,O(n^1)) * Step 1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: evenodd(x,0()) -> not(evenodd(x,s(0()))) evenodd(0(),s(0())) -> false() evenodd(s(x),s(0())) -> evenodd(x,0()) not(false()) -> true() not(true()) -> false() - Signature: {evenodd/2,not/1} / {0/0,false/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {evenodd,not} and constructors {0,false,s,true} + Applied Processor: NaturalMI {miDimension = 2, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing} + Details: We apply a matrix interpretation of kind constructor based matrix interpretation (containing no more than 1 non-zero interpretation-entries in the diagonal of the component-wise maxima): The following argument positions are considered usable: uargs(not) = {1} Following symbols are considered usable: {evenodd,not} TcT has computed the following interpretation: p(0) = [4] [8] p(evenodd) = [1 2] x1 + [0 2] x2 + [0] [0 0] [0 0] [4] p(false) = [4] [4] p(not) = [1 0] x1 + [2] [0 1] [0] p(s) = [1 2] x1 + [8] [0 0] [4] p(true) = [3] [4] Following rules are strictly oriented: evenodd(x,0()) = [1 2] x + [16] [0 0] [4] > [1 2] x + [10] [0 0] [4] = not(evenodd(x,s(0()))) evenodd(0(),s(0())) = [28] [4] > [4] [4] = false() evenodd(s(x),s(0())) = [1 2] x + [24] [0 0] [4] > [1 2] x + [16] [0 0] [4] = evenodd(x,0()) not(false()) = [6] [4] > [3] [4] = true() not(true()) = [5] [4] > [4] [4] = false() Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))