WORST_CASE(?,O(n^1)) * Step 1: NaturalPI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: add0(0(),x2) -> x2 add0(S(x),x2) -> +(S(0()),add0(x2,x)) - Weak TRS: +(x,S(0())) -> S(x) +(S(0()),y) -> S(y) - Signature: {+/2,add0/2} / {0/0,S/1} - Obligation: innermost runtime complexity wrt. defined symbols {+,add0} 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(+) = {2} Following symbols are considered usable: {+,add0} TcT has computed the following interpretation: p(+) = 1 + x1 + x2 p(0) = 1 p(S) = 2 + x1 p(add0) = 2 + 4*x1 + 4*x2 Following rules are strictly oriented: add0(0(),x2) = 6 + 4*x2 > x2 = x2 add0(S(x),x2) = 10 + 4*x + 4*x2 > 6 + 4*x + 4*x2 = +(S(0()),add0(x2,x)) Following rules are (at-least) weakly oriented: +(x,S(0())) = 4 + x >= 2 + x = S(x) +(S(0()),y) = 4 + y >= 2 + y = S(y) WORST_CASE(?,O(n^1))