WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: dbl(0(),y) -> y dbl(S(0()),S(0())) -> S(S(S(S(0())))) unsafe(0()) -> 0() unsafe(S(x)) -> dbl(unsafe(x),0()) - Signature: {dbl/2,unsafe/1} / {0/0,S/1} - Obligation: innermost runtime complexity wrt. defined symbols {dbl,unsafe} 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(0) 0 :: [] -(0)-> A(1) 0 :: [] -(0)-> A(4) S :: [A(0)] -(0)-> A(0) S :: [A(1)] -(1)-> A(1) S :: [A(4)] -(4)-> A(4) dbl :: [A(0) x A(1)] -(1)-> A(0) unsafe :: [A(4)] -(8)-> A(0) Cost-free Signatures used: -------------------------- 0 :: [] -(0)-> A_cf(0) S :: [A_cf(0)] -(0)-> A_cf(0) dbl :: [A_cf(0) x A_cf(0)] -(0)-> A_cf(0) unsafe :: [A_cf(0)] -(0)-> A_cf(0) Base Constructor Signatures used: --------------------------------- 0_A :: [] -(0)-> A(1) S_A :: [A(1)] -(1)-> A(1) * Step 2: Open MAYBE - Strict TRS: dbl(0(),y) -> y dbl(S(0()),S(0())) -> S(S(S(S(0())))) unsafe(0()) -> 0() unsafe(S(x)) -> dbl(unsafe(x),0()) - Signature: {dbl/2,unsafe/1} / {0/0,S/1} - Obligation: innermost runtime complexity wrt. defined symbols {dbl,unsafe} and constructors {0,S} Following problems could not be solved: - Strict TRS: dbl(0(),y) -> y dbl(S(0()),S(0())) -> S(S(S(S(0())))) unsafe(0()) -> 0() unsafe(S(x)) -> dbl(unsafe(x),0()) - Signature: {dbl/2,unsafe/1} / {0/0,S/1} - Obligation: innermost runtime complexity wrt. defined symbols {dbl,unsafe} and constructors {0,S} WORST_CASE(?,O(n^1))