WORST_CASE(?,O(n^1)) * Step 1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: dbl(0(),y) -> y dbl(S(0()),S(0())) -> S(S(S(S(0())))) unsafe(0()) -> 0() unsafe(S(x)) -> dbl(unsafe(x),0()) - Signature: {dbl/2,unsafe/1} / {0/0,S/1} - Obligation: innermost runtime complexity wrt. defined symbols {dbl,unsafe} 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(dbl) = {1} Following symbols are considered usable: {dbl,unsafe} TcT has computed the following interpretation: p(0) = [0] p(S) = [1] x1 + [2] p(dbl) = [1] x1 + [10] x2 + [1] p(unsafe) = [2] x1 + [1] Following rules are strictly oriented: dbl(0(),y) = [10] y + [1] > [1] y + [0] = y dbl(S(0()),S(0())) = [23] > [8] = S(S(S(S(0())))) unsafe(0()) = [1] > [0] = 0() unsafe(S(x)) = [2] x + [5] > [2] x + [2] = dbl(unsafe(x),0()) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))