WORST_CASE(?,O(n^2)) * Step 1: Ara WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: max(L(x)) -> x max(N(L(x),N(y,z))) -> max(N(L(x),L(max(N(y,z))))) max(N(L(0()),L(y))) -> y max(N(L(s(x)),L(s(y)))) -> s(max(N(L(x),L(y)))) - Signature: {max/1} / {0/0,L/1,N/2,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {max} and constructors {0,L,N,s} + Applied Processor: Ara {heuristics_ = NoHeuristics, minDegree = 1, maxDegree = 3, araTimeout = 60, araFindStrictRules = Nothing, araSmtSolver = MiniSMT} + Details: Signatures used: ---------------- 0 :: [] -(0)-> A(1, 0) L :: [A(5, 0)] -(4)-> A(1, 4) L :: [A(1, 0)] -(0)-> A(1, 0) L :: [A(5, 0)] -(0)-> A(5, 0) N :: [A(1, 0) x A(5, 0)] -(1)-> A(1, 4) N :: [A(5, 0) x A(5, 0)] -(5)-> A(5, 0) max :: [A(1, 4)] -(0)-> A(5, 0) s :: [A(1, 0)] -(1)-> A(1, 0) s :: [A(5, 0)] -(5)-> A(5, 0) Cost-free Signatures used: -------------------------- 0 :: [] -(0)-> A_cf(0, 0) L :: [A_cf(0, 0)] -(0)-> A_cf(0, 0) N :: [A_cf(0, 0) x A_cf(0, 0)] -(0)-> A_cf(0, 0) max :: [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) L_A :: [A(1, 0)] -(0)-> A(1, 0) L_A :: [A(1, 0)] -(1)-> A(0, 1) N_A :: [A(1, 0) x A(1, 0)] -(1)-> A(1, 0) N_A :: [A(0, 0) x A(1, 0)] -(0)-> A(0, 1) s_A :: [A(1, 0)] -(1)-> A(1, 0) s_A :: [A(0, 1)] -(0)-> A(0, 1) * Step 2: Open MAYBE - Strict TRS: max(L(x)) -> x max(N(L(x),N(y,z))) -> max(N(L(x),L(max(N(y,z))))) max(N(L(0()),L(y))) -> y max(N(L(s(x)),L(s(y)))) -> s(max(N(L(x),L(y)))) - Signature: {max/1} / {0/0,L/1,N/2,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {max} and constructors {0,L,N,s} Following problems could not be solved: - Strict TRS: max(L(x)) -> x max(N(L(x),N(y,z))) -> max(N(L(x),L(max(N(y,z))))) max(N(L(0()),L(y))) -> y max(N(L(s(x)),L(s(y)))) -> s(max(N(L(x),L(y)))) - Signature: {max/1} / {0/0,L/1,N/2,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {max} and constructors {0,L,N,s} WORST_CASE(?,O(n^2))