WORST_CASE(?,O(n^2)) * Step 1: Ara WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: -(x,0()) -> x -(s(x),s(y)) -> -(x,y) f(x,s(y)) -> f(p(-(x,s(y))),p(-(s(y),x))) f(s(x),y) -> f(p(-(s(x),y)),p(-(y,s(x)))) p(s(x)) -> x - Signature: {-/2,f/2,p/1} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {-,f,p} and constructors {0,s} + Applied Processor: Ara {araHeuristics = Heuristics, minDegree = 1, maxDegree = 2, araTimeout = 3, araRuleShifting = Nothing} + Details: Signatures used: ---------------- - :: ["A"(1, 6) x "A"(0, 0)] -(1)-> "A"(0, 6) 0 :: [] -(0)-> "A"(0, 0) f :: ["A"(6, 6) x "A"(6, 6)] -(0)-> "A"(0, 0) p :: ["A"(0, 6)] -(1)-> "A"(6, 6) s :: ["A"(7, 6)] -(1)-> "A"(1, 6) s :: ["A"(0, 0)] -(0)-> "A"(0, 0) s :: ["A"(12, 6)] -(6)-> "A"(6, 6) s :: ["A"(6, 6)] -(0)-> "A"(0, 6) Cost-free Signatures used: -------------------------- Base Constructor Signatures used: --------------------------------- "0_A" :: [] -(0)-> "A"(0) "s_A" :: ["A"(0)] -(0)-> "A"(0) WORST_CASE(?,O(n^2))