WORST_CASE(?,O(n^1)) * Step 1: NaturalPI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: dbl(0(),y) -> y dbl(S(0()),S(0())) -> S(S(S(S(0())))) save(0()) -> 0() save(S(x)) -> dbl(0(),save(x)) - Signature: {dbl/2,save/1} / {0/0,S/1} - Obligation: innermost runtime complexity wrt. defined symbols {dbl,save} and constructors {0,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(dbl) = {2} Following symbols are considered usable: {dbl,save} TcT has computed the following interpretation: p(0) = 1 p(S) = 4 + x1 p(dbl) = 3*x1 + x2 p(save) = 2 + 4*x1 Following rules are strictly oriented: dbl(0(),y) = 3 + y > y = y dbl(S(0()),S(0())) = 20 > 17 = S(S(S(S(0())))) save(0()) = 6 > 1 = 0() save(S(x)) = 18 + 4*x > 5 + 4*x = dbl(0(),save(x)) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))