WORST_CASE(?,O(n^1)) * Step 1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: foldr#3(Cons(x16,x6)) -> step_x_f(rev_l(),x16,foldr#3(x6)) foldr#3(Nil()) -> fleft_op_e_xs_1() main(Cons(x8,x9)) -> step_x_f#1(rev_l(),x8,foldr#3(x9),Nil()) main(Nil()) -> Nil() rev_l#2(x8,x10) -> Cons(x10,x8) step_x_f#1(rev_l(),x5,fleft_op_e_xs_1(),x3) -> rev_l#2(x3,x5) step_x_f#1(rev_l(),x5,step_x_f(x2,x3,x4),x1) -> step_x_f#1(x2,x3,x4,rev_l#2(x1,x5)) - Signature: {foldr#3/1,main/1,rev_l#2/2,step_x_f#1/4} / {Cons/2,Nil/0,fleft_op_e_xs_1/0,rev_l/0,step_x_f/3} - Obligation: innermost runtime complexity wrt. defined symbols {foldr#3,main,rev_l#2,step_x_f#1} and constructors {Cons ,Nil,fleft_op_e_xs_1,rev_l,step_x_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(step_x_f) = {3}, uargs(step_x_f#1) = {3,4} Following symbols are considered usable: {foldr#3,main,rev_l#2,step_x_f#1} TcT has computed the following interpretation: p(Cons) = [1] x2 + [2] p(Nil) = [0] p(fleft_op_e_xs_1) = [0] p(foldr#3) = [9] x1 + [8] p(main) = [12] x1 + [7] p(rev_l) = [4] p(rev_l#2) = [1] x1 + [3] p(step_x_f) = [1] x1 + [1] x3 + [10] p(step_x_f#1) = [1] x1 + [1] x3 + [1] x4 + [2] Following rules are strictly oriented: foldr#3(Cons(x16,x6)) = [9] x6 + [26] > [9] x6 + [22] = step_x_f(rev_l(),x16,foldr#3(x6)) foldr#3(Nil()) = [8] > [0] = fleft_op_e_xs_1() main(Cons(x8,x9)) = [12] x9 + [31] > [9] x9 + [14] = step_x_f#1(rev_l(),x8,foldr#3(x9),Nil()) main(Nil()) = [7] > [0] = Nil() rev_l#2(x8,x10) = [1] x8 + [3] > [1] x8 + [2] = Cons(x10,x8) step_x_f#1(rev_l(),x5,fleft_op_e_xs_1(),x3) = [1] x3 + [6] > [1] x3 + [3] = rev_l#2(x3,x5) step_x_f#1(rev_l(),x5,step_x_f(x2,x3,x4),x1) = [1] x1 + [1] x2 + [1] x4 + [16] > [1] x1 + [1] x2 + [1] x4 + [5] = step_x_f#1(x2,x3,x4,rev_l#2(x1,x5)) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))