WORST_CASE(?,O(n^1)) * Step 1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: a__b() -> a() a__b() -> b() a__f(X1,X2,X3) -> f(X1,X2,X3) a__f(a(),X,X) -> a__f(X,a__b(),b()) mark(a()) -> a() mark(b()) -> a__b() mark(f(X1,X2,X3)) -> a__f(X1,mark(X2),X3) - Signature: {a__b/0,a__f/3,mark/1} / {a/0,b/0,f/3} - Obligation: innermost runtime complexity wrt. defined symbols {a__b,a__f,mark} and constructors {a,b,f} + 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(a__f) = {2} Following symbols are considered usable: {a__b,a__f,mark} TcT has computed the following interpretation: p(a) = [3] p(a__b) = [8] p(a__f) = [3] x1 + [1] x2 + [2] x3 + [7] p(b) = [0] p(f) = [1] x1 + [1] x2 + [1] x3 + [2] p(mark) = [4] x1 + [10] Following rules are strictly oriented: a__b() = [8] > [3] = a() a__b() = [8] > [0] = b() a__f(X1,X2,X3) = [3] X1 + [1] X2 + [2] X3 + [7] > [1] X1 + [1] X2 + [1] X3 + [2] = f(X1,X2,X3) a__f(a(),X,X) = [3] X + [16] > [3] X + [15] = a__f(X,a__b(),b()) mark(a()) = [22] > [3] = a() mark(b()) = [10] > [8] = a__b() mark(f(X1,X2,X3)) = [4] X1 + [4] X2 + [4] X3 + [18] > [3] X1 + [4] X2 + [2] X3 + [17] = a__f(X1,mark(X2),X3) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))