WORST_CASE(?,O(n^1)) * Step 1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: minus(x,0()) -> x minus(s(x),s(y)) -> minus(x,y) quot(0(),s(y)) -> 0() quot(s(x),s(y)) -> s(quot(minus(x,y),s(y))) - Signature: {minus/2,quot/2} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {minus,quot} 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(quot) = {1}, uargs(s) = {1} Following symbols are considered usable: {minus,quot} TcT has computed the following interpretation: p(0) = [9] p(minus) = [1] x1 + [1] p(quot) = [2] x1 + [6] p(s) = [1] x1 + [4] Following rules are strictly oriented: minus(x,0()) = [1] x + [1] > [1] x + [0] = x minus(s(x),s(y)) = [1] x + [5] > [1] x + [1] = minus(x,y) quot(0(),s(y)) = [24] > [9] = 0() quot(s(x),s(y)) = [2] x + [14] > [2] x + [12] = s(quot(minus(x,y),s(y))) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))