WORST_CASE(?,O(n^1)) * Step 1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: div(0(),s(Y)) -> 0() div(s(X),s(Y)) -> s(div(minus(X,Y),s(Y))) minus(X,0()) -> X minus(s(X),s(Y)) -> p(minus(X,Y)) p(s(X)) -> X - Signature: {div/2,minus/2,p/1} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {div,minus,p} 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(div) = {1}, uargs(p) = {1}, uargs(s) = {1} Following symbols are considered usable: {div,minus,p} TcT has computed the following interpretation: p(0) = [2] p(div) = [10] x1 + [0] p(minus) = [1] x1 + [1] p(p) = [1] x1 + [1] p(s) = [1] x1 + [2] Following rules are strictly oriented: div(0(),s(Y)) = [20] > [2] = 0() div(s(X),s(Y)) = [10] X + [20] > [10] X + [12] = s(div(minus(X,Y),s(Y))) minus(X,0()) = [1] X + [1] > [1] X + [0] = X minus(s(X),s(Y)) = [1] X + [3] > [1] X + [2] = p(minus(X,Y)) p(s(X)) = [1] X + [3] > [1] X + [0] = X Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))