WORST_CASE(?,O(n^1)) * Step 1: NaturalPI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: half(0()) -> 0() half(s(s(x))) -> s(half(x)) log(s(0())) -> 0() log(s(s(x))) -> s(log(s(half(x)))) - Signature: {half/1,log/1} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {half,log} 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(log) = {1}, uargs(s) = {1} Following symbols are considered usable: {half,log} TcT has computed the following interpretation: p(0) = 4 p(half) = 1 + x1 p(log) = 12 + 2*x1 p(s) = 4 + x1 Following rules are strictly oriented: half(0()) = 5 > 4 = 0() half(s(s(x))) = 9 + x > 5 + x = s(half(x)) log(s(0())) = 28 > 4 = 0() log(s(s(x))) = 28 + 2*x > 26 + 2*x = s(log(s(half(x)))) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))