WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: activate(X) -> X and(tt(),X) -> activate(X) plus(N,0()) -> N plus(N,s(M)) -> s(plus(N,M)) - Signature: {activate/1,and/2,plus/2} / {0/0,s/1,tt/0} - Obligation: innermost runtime complexity wrt. defined symbols {activate,and,plus} and constructors {0,s,tt} + Applied Processor: Ara {heuristics_ = NoHeuristics, minDegree = 1, maxDegree = 3, araTimeout = 60, araFindStrictRules = Nothing, araSmtSolver = MiniSMT} + Details: Signatures used: ---------------- 0 :: [] -(0)-> A(4) activate :: [A(0)] -(4)-> A(0) and :: [A(0) x A(0)] -(12)-> A(0) plus :: [A(1) x A(4)] -(2)-> A(1) s :: [A(4)] -(4)-> A(4) s :: [A(1)] -(1)-> A(1) tt :: [] -(0)-> A(0) Cost-free Signatures used: -------------------------- 0 :: [] -(0)-> A_cf(0) plus :: [A_cf(0) x A_cf(0)] -(0)-> A_cf(0) s :: [A_cf(0)] -(0)-> A_cf(0) Base Constructor Signatures used: --------------------------------- 0_A :: [] -(0)-> A(1) s_A :: [A(1)] -(1)-> A(1) tt_A :: [] -(0)-> A(1) * Step 2: Open MAYBE - Strict TRS: activate(X) -> X and(tt(),X) -> activate(X) plus(N,0()) -> N plus(N,s(M)) -> s(plus(N,M)) - Signature: {activate/1,and/2,plus/2} / {0/0,s/1,tt/0} - Obligation: innermost runtime complexity wrt. defined symbols {activate,and,plus} and constructors {0,s,tt} Following problems could not be solved: - Strict TRS: activate(X) -> X and(tt(),X) -> activate(X) plus(N,0()) -> N plus(N,s(M)) -> s(plus(N,M)) - Signature: {activate/1,and/2,plus/2} / {0/0,s/1,tt/0} - Obligation: innermost runtime complexity wrt. defined symbols {activate,and,plus} and constructors {0,s,tt} WORST_CASE(?,O(n^1))