WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: U11(tt(),M,N) -> U12(tt(),activate(M),activate(N)) U12(tt(),M,N) -> s(plus(activate(N),activate(M))) activate(X) -> X plus(N,0()) -> N plus(N,s(M)) -> U11(tt(),M,N) - Signature: {U11/3,U12/3,activate/1,plus/2} / {0/0,s/1,tt/0} - Obligation: innermost runtime complexity wrt. defined symbols {U11,U12,activate,plus} and constructors {0,s,tt} + Applied Processor: Ara {heuristics_ = NoHeuristics, minDegree = 1, maxDegree = 3, araTimeout = 60, araFindStrictRules = Nothing, araSmtSolver = Z3} + Details: Signatures used: ---------------- 0 :: [] -(0)-> A(9) U11 :: [A(2) x A(9) x A(9)] -(14)-> A(0) U12 :: [A(2) x A(9) x A(9)] -(11)-> A(0) activate :: [A(9)] -(1)-> A(9) plus :: [A(9) x A(9)] -(8)-> A(0) s :: [A(9)] -(9)-> A(9) s :: [A(0)] -(0)-> A(0) tt :: [] -(0)-> A(2) tt :: [] -(0)-> A(13) tt :: [] -(0)-> A(12) Cost-free Signatures used: -------------------------- 0 :: [] -(0)-> A_cf(0) U11 :: [A_cf(0) x A_cf(0) x A_cf(0)] -(0)-> A_cf(0) U12 :: [A_cf(0) x A_cf(0) x A_cf(0)] -(0)-> A_cf(0) activate :: [A_cf(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) tt :: [] -(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: U11(tt(),M,N) -> U12(tt(),activate(M),activate(N)) U12(tt(),M,N) -> s(plus(activate(N),activate(M))) activate(X) -> X plus(N,0()) -> N plus(N,s(M)) -> U11(tt(),M,N) - Signature: {U11/3,U12/3,activate/1,plus/2} / {0/0,s/1,tt/0} - Obligation: innermost runtime complexity wrt. defined symbols {U11,U12,activate,plus} and constructors {0,s,tt} Following problems could not be solved: - Strict TRS: U11(tt(),M,N) -> U12(tt(),activate(M),activate(N)) U12(tt(),M,N) -> s(plus(activate(N),activate(M))) activate(X) -> X plus(N,0()) -> N plus(N,s(M)) -> U11(tt(),M,N) - Signature: {U11/3,U12/3,activate/1,plus/2} / {0/0,s/1,tt/0} - Obligation: innermost runtime complexity wrt. defined symbols {U11,U12,activate,plus} and constructors {0,s,tt} WORST_CASE(?,O(n^1))