WORST_CASE(?,O(n^1)) * Step 1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: implies(x,or(y,z)) -> or(y,implies(x,z)) implies(not(x),y) -> or(x,y) implies(not(x),or(y,z)) -> implies(y,or(x,z)) - Signature: {implies/2} / {not/1,or/2} - Obligation: innermost runtime complexity wrt. defined symbols {implies} and constructors {not,or} + 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(or) = {2} Following symbols are considered usable: {implies} TcT has computed the following interpretation: p(implies) = [2] x1 + [2] x2 + [2] p(not) = [1] x1 + [1] p(or) = [1] x1 + [1] x2 + [1] Following rules are strictly oriented: implies(x,or(y,z)) = [2] x + [2] y + [2] z + [4] > [2] x + [1] y + [2] z + [3] = or(y,implies(x,z)) implies(not(x),y) = [2] x + [2] y + [4] > [1] x + [1] y + [1] = or(x,y) implies(not(x),or(y,z)) = [2] x + [2] y + [2] z + [6] > [2] x + [2] y + [2] z + [4] = implies(y,or(x,z)) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))