WORST_CASE(?,O(n^1)) * Step 1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(g(h(a(),b()),c()),d()) -> if(e(),f(.(b(),g(h(a(),b()),c())),d()),f(c(),d'())) f(g(i(a(),b(),b'()),c()),d()) -> if(e(),f(.(b(),c()),d'()),f(.(b'(),c()),d'())) - Signature: {f/2} / {./2,a/0,b/0,b'/0,c/0,d/0,d'/0,e/0,g/2,h/2,i/3,if/3} - Obligation: innermost runtime complexity wrt. defined symbols {f} and constructors {.,a,b,b',c,d,d',e,g,h,i,if} + 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: none Following symbols are considered usable: {f} TcT has computed the following interpretation: p(.) = [1] x1 + [1] x2 + [0] p(a) = [0] p(b) = [0] p(b') = [0] p(c) = [0] p(d) = [0] p(d') = [0] p(e) = [0] p(f) = [11] p(g) = [0] p(h) = [8] p(i) = [8] p(if) = [3] Following rules are strictly oriented: f(g(h(a(),b()),c()),d()) = [11] > [3] = if(e(),f(.(b(),g(h(a(),b()),c())),d()),f(c(),d'())) f(g(i(a(),b(),b'()),c()),d()) = [11] > [3] = if(e(),f(.(b(),c()),d'()),f(.(b'(),c()),d'())) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))