WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(x,g(y,z)) -> g(f(x,y),z) f(x,nil()) -> g(nil(),x) norm(g(x,y)) -> s(norm(x)) norm(nil()) -> 0() rem(g(x,y),0()) -> g(x,y) rem(g(x,y),s(z)) -> rem(x,z) rem(nil(),y) -> nil() - Signature: {f/2,norm/1,rem/2} / {0/0,g/2,nil/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f,norm,rem} and constructors {0,g,nil,s} + Applied Processor: Ara {araHeuristics = NoHeuristics, minDegree = 1, maxDegree = 2, araTimeout = 5, araRuleShifting = Nothing} + Details: Signatures used: ---------------- 0 :: [] -(0)-> "A"(9) 0 :: [] -(0)-> "A"(14) f :: ["A"(12) x "A"(8)] -(8)-> "A"(0) g :: ["A"(8) x "A"(0)] -(8)-> "A"(8) g :: ["A"(15) x "A"(0)] -(15)-> "A"(15) g :: ["A"(0) x "A"(0)] -(0)-> "A"(0) nil :: [] -(0)-> "A"(8) nil :: [] -(0)-> "A"(15) nil :: [] -(0)-> "A"(0) nil :: [] -(0)-> "A"(14) norm :: ["A"(15)] -(1)-> "A"(4) rem :: ["A"(0) x "A"(9)] -(8)-> "A"(0) s :: ["A"(9)] -(9)-> "A"(9) s :: ["A"(4)] -(4)-> "A"(4) Cost-free Signatures used: -------------------------- Base Constructor Signatures used: --------------------------------- "0_A" :: [] -(0)-> "A"(1) "g_A" :: ["A"(1) x "A"(0)] -(1)-> "A"(1) "nil_A" :: [] -(0)-> "A"(1) "s_A" :: ["A"(1)] -(1)-> "A"(1) WORST_CASE(?,O(n^1))