WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: conv(0()) -> cons(nil(),0()) conv(s(x)) -> cons(conv(half(s(x))),lastbit(s(x))) half(0()) -> 0() half(s(0())) -> 0() half(s(s(x))) -> s(half(x)) lastbit(0()) -> 0() lastbit(s(0())) -> s(0()) lastbit(s(s(x))) -> lastbit(x) - Signature: {conv/1,half/1,lastbit/1} / {0/0,cons/2,nil/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {conv,half,lastbit} and constructors {0,cons,nil,s} + Applied Processor: Ara {heuristics_ = NoHeuristics, minDegree = 1, maxDegree = 3, araTimeout = 60, araFindStrictRules = Nothing, araSmtSolver = Z3} + Details: Signatures used: ---------------- 0 :: [] -(0)-> A(11) 0 :: [] -(0)-> A(6) 0 :: [] -(0)-> A(1) 0 :: [] -(0)-> A(13) 0 :: [] -(0)-> A(7) cons :: [A(0) x A(0)] -(0)-> A(0) cons :: [A(0) x A(0)] -(0)-> A(1) conv :: [A(11)] -(1)-> A(0) half :: [A(6)] -(1)-> A(11) lastbit :: [A(1)] -(1)-> A(0) nil :: [] -(0)-> A(12) s :: [A(11)] -(11)-> A(11) s :: [A(6)] -(6)-> A(6) s :: [A(1)] -(1)-> A(1) s :: [A(0)] -(0)-> A(0) Cost-free Signatures used: -------------------------- 0 :: [] -(0)-> A_cf(0) cons :: [A_cf(0) x A_cf(0)] -(0)-> A_cf(0) conv :: [A_cf(0)] -(0)-> A_cf(0) half :: [A_cf(0)] -(0)-> A_cf(0) lastbit :: [A_cf(0)] -(0)-> A_cf(0) nil :: [] -(0)-> A_cf(0) s :: [A_cf(0)] -(0)-> A_cf(0) Base Constructor Signatures used: --------------------------------- 0_A :: [] -(0)-> A(1) cons_A :: [A(0) x A(0)] -(0)-> A(1) nil_A :: [] -(0)-> A(1) s_A :: [A(1)] -(1)-> A(1) * Step 2: Open MAYBE - Strict TRS: conv(0()) -> cons(nil(),0()) conv(s(x)) -> cons(conv(half(s(x))),lastbit(s(x))) half(0()) -> 0() half(s(0())) -> 0() half(s(s(x))) -> s(half(x)) lastbit(0()) -> 0() lastbit(s(0())) -> s(0()) lastbit(s(s(x))) -> lastbit(x) - Signature: {conv/1,half/1,lastbit/1} / {0/0,cons/2,nil/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {conv,half,lastbit} and constructors {0,cons,nil,s} Following problems could not be solved: - Strict TRS: conv(0()) -> cons(nil(),0()) conv(s(x)) -> cons(conv(half(s(x))),lastbit(s(x))) half(0()) -> 0() half(s(0())) -> 0() half(s(s(x))) -> s(half(x)) lastbit(0()) -> 0() lastbit(s(0())) -> s(0()) lastbit(s(s(x))) -> lastbit(x) - Signature: {conv/1,half/1,lastbit/1} / {0/0,cons/2,nil/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {conv,half,lastbit} and constructors {0,cons,nil,s} WORST_CASE(?,O(n^1))