WORST_CASE(?,O(n^1)) * Step 1: NaturalPI 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: NaturalPI {shape = Linear, restrict = NoRestrict, uargs = UArgs, urules = URules, selector = Nothing} + Details: We apply a polynomial interpretation of kind constructor-based(linear): 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) = 2 + x2 p(Nil) = 4 p(fleft_op_e_xs_1) = 8 p(foldr#3) = 4*x1 p(main) = 7 + 4*x1 p(rev_l) = 1 p(rev_l#2) = 3 + x1 p(step_x_f) = 4 + x1 + x3 p(step_x_f#1) = x3 + x4 Following rules are strictly oriented: foldr#3(Cons(x16,x6)) = 8 + 4*x6 > 5 + 4*x6 = step_x_f(rev_l(),x16,foldr#3(x6)) foldr#3(Nil()) = 16 > 8 = fleft_op_e_xs_1() main(Cons(x8,x9)) = 15 + 4*x9 > 4 + 4*x9 = step_x_f#1(rev_l(),x8,foldr#3(x9),Nil()) main(Nil()) = 23 > 4 = Nil() rev_l#2(x8,x10) = 3 + x8 > 2 + x8 = Cons(x10,x8) step_x_f#1(rev_l(),x5,fleft_op_e_xs_1(),x3) = 8 + x3 > 3 + x3 = rev_l#2(x3,x5) step_x_f#1(rev_l(),x5,step_x_f(x2,x3,x4),x1) = 4 + x1 + x2 + x4 > 3 + x1 + x4 = step_x_f#1(x2,x3,x4,rev_l#2(x1,x5)) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))