WORST_CASE(?,O(n^2)) * Step 1: Ara WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: f(0()) -> 0() f(s(x)) -> s(s(f(p(s(x))))) p(s(x)) -> x - Signature: {f/1,p/1} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f,p} and constructors {0,s} + Applied Processor: Ara {heuristics_ = NoHeuristics, minDegree = 1, maxDegree = 3, araTimeout = 60, araFindStrictRules = Nothing, araSmtSolver = MiniSMT} + Details: Signatures used: ---------------- 0 :: [] -(0)-> A(2, 8) 0 :: [] -(0)-> A(8, 2) f :: [A(2, 8)] -(8)-> A(0, 0) p :: [A(0, 8)] -(1)-> A(2, 8) s :: [A(8, 8)] -(2)-> A(2, 8) s :: [A(8, 8)] -(0)-> A(0, 8) s :: [A(0, 0)] -(0)-> A(0, 0) Cost-free Signatures used: -------------------------- 0 :: [] -(0)-> A_cf(0, 0) f :: [A_cf(0, 0)] -(0)-> A_cf(0, 0) p :: [A_cf(0, 0)] -(0)-> A_cf(0, 0) s :: [A_cf(0, 0)] -(0)-> A_cf(0, 0) Base Constructor Signatures used: --------------------------------- 0_A :: [] -(0)-> A(1, 0) 0_A :: [] -(0)-> A(0, 1) s_A :: [A(0, 0)] -(1)-> A(1, 0) s_A :: [A(1, 1)] -(0)-> A(0, 1) * Step 2: Open MAYBE - Strict TRS: f(0()) -> 0() f(s(x)) -> s(s(f(p(s(x))))) p(s(x)) -> x - Signature: {f/1,p/1} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f,p} and constructors {0,s} Following problems could not be solved: - Strict TRS: f(0()) -> 0() f(s(x)) -> s(s(f(p(s(x))))) p(s(x)) -> x - Signature: {f/1,p/1} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f,p} and constructors {0,s} WORST_CASE(?,O(n^2))