WORST_CASE(?,O(n^1)) * Step 1: NaturalPI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: ackin(s(X),s(Y)) -> u21(ackin(s(X),Y),X) u21(ackout(X),Y) -> u22(ackin(Y,X)) - Signature: {ackin/2,u21/2} / {ackout/1,s/1,u22/1} - Obligation: innermost runtime complexity wrt. defined symbols {ackin,u21} and constructors {ackout,s,u22} + 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(u21) = {1}, uargs(u22) = {1} Following symbols are considered usable: {ackin,u21} TcT has computed the following interpretation: p(ackin) = 8 + x2 p(ackout) = 13 + x1 p(s) = 8 + x1 p(u21) = 3 + x1 p(u22) = 4 + x1 Following rules are strictly oriented: ackin(s(X),s(Y)) = 16 + Y > 11 + Y = u21(ackin(s(X),Y),X) u21(ackout(X),Y) = 16 + X > 12 + X = u22(ackin(Y,X)) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))