WORST_CASE(?,O(n^1)) * Step 1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: merge(x,nil()) -> x merge(++(x,y),++(u(),v())) -> ++(x,merge(y,++(u(),v()))) merge(++(x,y),++(u(),v())) -> ++(u(),merge(++(x,y),v())) merge(nil(),y) -> y - Signature: {merge/2} / {++/2,nil/0,u/0,v/0} - Obligation: innermost runtime complexity wrt. defined symbols {merge} and constructors {++,nil,u,v} + 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(++) = {2} Following symbols are considered usable: {merge} TcT has computed the following interpretation: p(++) = [1] x2 + [2] p(merge) = [4] x1 + [6] x2 + [2] p(nil) = [4] p(u) = [0] p(v) = [0] Following rules are strictly oriented: merge(x,nil()) = [4] x + [26] > [1] x + [0] = x merge(++(x,y),++(u(),v())) = [4] y + [22] > [4] y + [16] = ++(x,merge(y,++(u(),v()))) merge(++(x,y),++(u(),v())) = [4] y + [22] > [4] y + [12] = ++(u(),merge(++(x,y),v())) merge(nil(),y) = [6] y + [18] > [1] y + [0] = y Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))