WORST_CASE(?,O(n^1)) * Step 1: NaturalPI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: sqr(x) -> *(x,x) sum(0()) -> 0() sum(s(x)) -> +(*(s(x),s(x)),sum(x)) sum(s(x)) -> +(sqr(s(x)),sum(x)) - Signature: {sqr/1,sum/1} / {*/2,+/2,0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {sqr,sum} and constructors {*,+,0,s} + Applied Processor: NaturalPI {shape = StronglyLinear, restrict = NoRestrict, uargs = UArgs, urules = URules, selector = Nothing} + Details: We apply a polynomial interpretation of kind constructor-based(stronglyLinear): The following argument positions are considered usable: uargs(+) = {1,2} Following symbols are considered usable: {sqr,sum} TcT has computed the following interpretation: p(*) = 4 p(+) = x1 + x2 p(0) = 5 p(s) = 8 + x1 p(sqr) = 6 p(sum) = 8 + x1 Following rules are strictly oriented: sqr(x) = 6 > 4 = *(x,x) sum(0()) = 13 > 5 = 0() sum(s(x)) = 16 + x > 12 + x = +(*(s(x),s(x)),sum(x)) sum(s(x)) = 16 + x > 14 + x = +(sqr(s(x)),sum(x)) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))