WORST_CASE(?,O(n^1)) * Step 1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: sqr(x) -> *(x,x) sum(0()) -> 0() sum(s(x)) -> +(*(s(x),s(x)),sum(x)) sum(s(x)) -> +(sqr(s(x)),sum(x)) - Signature: {sqr/1,sum/1} / {*/2,+/2,0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {sqr,sum} 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(+) = {1,2} Following symbols are considered usable: {sqr,sum} TcT has computed the following interpretation: p(*) = [0] p(+) = [1] x1 + [1] x2 + [6] p(0) = [2] p(s) = [1] x1 + [4] p(sqr) = [8] p(sum) = [4] x1 + [0] Following rules are strictly oriented: sqr(x) = [8] > [0] = *(x,x) sum(0()) = [8] > [2] = 0() sum(s(x)) = [4] x + [16] > [4] x + [6] = +(*(s(x),s(x)),sum(x)) sum(s(x)) = [4] x + [16] > [4] x + [14] = +(sqr(s(x)),sum(x)) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))