WORST_CASE(?,O(n^1)) * Step 1: NaturalPI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(0()) -> cons(0()) f(s(0())) -> f(p(s(0()))) p(s(0())) -> 0() - Signature: {f/1,p/1} / {0/0,cons/1,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f,p} and constructors {0,cons,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(f) = {1} Following symbols are considered usable: {f,p} TcT has computed the following interpretation: p(0) = 3 p(cons) = 0 p(f) = 2*x1 p(p) = 8 p(s) = 9 + x1 Following rules are strictly oriented: f(0()) = 6 > 0 = cons(0()) f(s(0())) = 24 > 16 = f(p(s(0()))) p(s(0())) = 8 > 3 = 0() Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))