WORST_CASE(?,O(n^1)) * Step 1: NaturalPI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: fold#3(Cons(x4,x2)) -> plus#2(x4,fold#3(x2)) fold#3(Nil()) -> 0() main(x1) -> fold#3(x1) plus#2(0(),x12) -> x12 plus#2(S(x4),x2) -> S(plus#2(x4,x2)) - Signature: {fold#3/1,main/1,plus#2/2} / {0/0,Cons/2,Nil/0,S/1} - Obligation: innermost runtime complexity wrt. defined symbols {fold#3,main,plus#2} and constructors {0,Cons,Nil,S} + 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(S) = {1}, uargs(plus#2) = {2} Following symbols are considered usable: {fold#3,main,plus#2} TcT has computed the following interpretation: p(0) = 4 p(Cons) = 2 + x1 + x2 p(Nil) = 8 p(S) = 10 + x1 p(fold#3) = 2*x1 p(main) = 3 + 9*x1 p(plus#2) = 2 + 2*x1 + x2 Following rules are strictly oriented: fold#3(Cons(x4,x2)) = 4 + 2*x2 + 2*x4 > 2 + 2*x2 + 2*x4 = plus#2(x4,fold#3(x2)) fold#3(Nil()) = 16 > 4 = 0() main(x1) = 3 + 9*x1 > 2*x1 = fold#3(x1) plus#2(0(),x12) = 10 + x12 > x12 = x12 plus#2(S(x4),x2) = 22 + x2 + 2*x4 > 12 + x2 + 2*x4 = S(plus#2(x4,x2)) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))