WORST_CASE(?,O(n^2)) * Step 1: NaturalPI WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: plus(plus(X,Y),Z) -> plus(X,plus(Y,Z)) times(X,s(Y)) -> plus(X,times(Y,X)) - Signature: {plus/2,times/2} / {s/1} - Obligation: innermost runtime complexity wrt. defined symbols {plus,times} and constructors {s} + Applied Processor: NaturalPI {shape = Quadratic, restrict = NoRestrict, uargs = UArgs, urules = URules, selector = Nothing} + Details: We apply a polynomial interpretation of kind constructor-based(quadratic): The following argument positions are considered usable: uargs(plus) = {2} Following symbols are considered usable: {plus,times} TcT has computed the following interpretation: p(plus) = 1 + 2*x1 + x2 p(s) = 2 + x1 p(times) = 2*x1 + x1^2 + x2^2 Following rules are strictly oriented: plus(plus(X,Y),Z) = 3 + 4*X + 2*Y + Z > 2 + 2*X + 2*Y + Z = plus(X,plus(Y,Z)) times(X,s(Y)) = 4 + 2*X + X^2 + 4*Y + Y^2 > 1 + 2*X + X^2 + 2*Y + Y^2 = plus(X,times(Y,X)) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^2))